nigel.stanger / Digital_Repository
Transfer to URL with SHA Find file
Newer
Older
Digital_Repository / Misc / Mass downloads / UTas / 1911.html
Nigel Stanger on 7 May 2013 25 KB - Imported Misc directory.
Raw Blame History 
  1. <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
  2. "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
  3. <html>
  4.   <head>
  5.     <title>UTas ePrints - Dual Symmetric Inverse Monoids and Representation Theory</title>
  6.     <script type="text/javascript" src="http://eprints.utas.edu.au/javascript/auto.js"><!-- padder --></script>
  7.     <style type="text/css" media="screen">@import url(http://eprints.utas.edu.au/style/auto.css);</style>
  8.     <style type="text/css" media="print">@import url(http://eprints.utas.edu.au/style/print.css);</style>
  9.     <link rel="icon" href="/images/eprints/favicon.ico" type="image/x-icon" />
  10.     <link rel="shortcut icon" href="/images/eprints/favicon.ico" type="image/x-icon" />
  11.     <link rel="Top" href="http://eprints.utas.edu.au/" />
  12.     <link rel="Search" href="http://eprints.utas.edu.au/cgi/search" />
  13.     <meta content="FitzGerald, D.G." name="eprints.creators_name" />
  14. <meta content="Leech, Jonathan" name="eprints.creators_name" />
  15. <meta content="D.FitzGerald@utas.edu.au" name="eprints.creators_id" />
  16. <meta content="leech@westmont.edu" name="eprints.creators_id" />
  17. <meta content="article" name="eprints.type" />
  18. <meta content="2007-09-17" name="eprints.datestamp" />
  19. <meta content="2008-02-07T01:22:06Z" name="eprints.lastmod" />
  20. <meta content="show" name="eprints.metadata_visibility" />
  21. <meta content="Dual Symmetric Inverse Monoids and Representation Theory" name="eprints.title" />
  22. <meta content="pub" name="eprints.ispublished" />
  23. <meta content="230105" name="eprints.subjects" />
  24. <meta content="restricted" name="eprints.full_text_status" />
  25. <meta content="dual symmetric inverse monoid, representations of inverse semigroups" name="eprints.keywords" />
  26. <meta content="There is a substantial theory (modelled on permutation representations of groups) of representations of an
  27. inverse semigroup S in a symmetric inverse monoid I_X , that is, a monoid of partial one-to-one self-maps
  28. of a set X. The present paper describes the structure of a categorical dual I*_X to the symmetric inverse
  29. monoid and discusses representations of an inverse semigroup in this dual symmetric inverse monoid. It
  30. is shown how a representation of S by (full) selfmaps of a set X leads to dual pairs of representations
  31. in I_X and I*_X, and how a number of known representations arise as one or the other of these pairs.
  32. Conditions on S are described which ensure that representations of S preserve such infima or suprema as
  33. exist in the natural order of S. The categorical treatment allows the construction, from standard functors,
  34. of representations of S in certain other inverse algebras (that is, inverse monoids in which all finite infima
  35. exist). The paper concludes by distinguishing two subclasses of inverse algebras on the basis of their
  36. embedding properties." name="eprints.abstract" />
  37. <meta content="1998" name="eprints.date" />
  38. <meta content="published" name="eprints.date_type" />
  39. <meta content="Journal of the Australian Mathematical Society, Series A" name="eprints.publication" />
  40. <meta content="64" name="eprints.volume" />
  41. <meta content="3" name="eprints.number" />
  42. <meta content="345-367" name="eprints.pagerange" />
  43. <meta content="UNSPECIFIED" name="eprints.thesis_type" />
  44. <meta content="TRUE" name="eprints.refereed" />
  45. <meta content="0263-6115" name="eprints.issn" />
  46. <meta content="http://www.austms.org.au/Publ/Jamsa/V64P3/pdf/e07.pdf" name="eprints.official_url" />
  47. <meta content="[1] D. A. Bredikhin, Representations of inverse semigroups by difunctional multipermutations, in:
  48. Transformation Semigroups: Proceedings of the International Conference held at the University of
  49. Essex, Colchester, England, August 3rd-6th, 1993 (ed. P. M. Higgins) (Department of Mathematics,
  50. University of Essex, 1994) pp. 1-10.
  51. [2] B. Fichtner, Ueber die zu Gruppen gehoerigen induktiven Gruppoide, I, Math. Nachr. 44 (1970),
  52. 313-339.
  53. [3] B. Fichtner-Schultz,
  54. Ueber die zu Gruppen gehoerigen induktiven Gruppoide, II, Math. Nachr. 48
  55. (1971), 275-278.
  56. [4] P. A. Grillet, Semigroups: an introduction to the structure theory (Marcel Dekker, New York,
  57. 1995).
  58. [5] P. J. Hilton and U. Stammbach, A course in homological algebra, Graduate Texts in Math. 4
  59. (Springer, New York, 1971).
  60. [6] J. Leech, Constructing inverse monoids from small categories, Semigroup Forum 36 (1987),
  61. 89-116.
  62. [7] J. Leech, Inverse monoids with a natural semilattice ordering, Proc. London Math. Soc. 70 (1995),
  63. 146-182.
  64. [8] J. Leech, On the foundations of inverse monoids and inverse algebras, Proc. Edinburgh Math. Soc.
  65. 41 (1998), 1-21.
  66. [9] S. Mac Lane, Categories for the working mathematician, Graduate Texts in Math. 5 (Springer,
  67. New York, 1971).
  68. [10] M. Petrich, Inverse semigroups (Wiley, New York, 1984).
  69. [11] G. B. Preston, Representations of inverse semigroups by one-to-one
  70. partial transformations of a
  71. set, Semigroup Forum 6 (1973), 240-245; Addendum, Semigroup Forum 8 (1974), 277.
  72. [12] J. Riguet, Relations binaires, fermetures, correspondances de Galois, Bull. Soc. Math. France 76
  73. (1948), 114-132.
  74. [13] B. M. Schein, Representation of inverse semigroups by local automorphisms and multiautomorphisms
  75. of groups and rings, Semigroup Forum 32 (1985), 55-60.
  76. [14] B. M. Schein, Multigroups, J. Algebra 111 (1987), 114-132.
  77. [15] V. V. Wagner, Theory of generalised grouds and generalised groups, Mat. Sb. (NS) 32 (1953),
  78. 545-632." name="eprints.referencetext" />
  79. <meta content="FitzGerald, D.G. and Leech, Jonathan (1998) Dual Symmetric Inverse Monoids and Representation Theory. Journal of the Australian Mathematical Society, Series A, 64 (3). pp. 345-367. ISSN 0263-6115" name="eprints.citation" />
  80. <meta content="http://eprints.utas.edu.au/1911/1/FL98.pdf" name="eprints.document_url" />
  81. <link rel="schema.DC" href="http://purl.org/DC/elements/1.0/" />
  82. <meta content="Dual Symmetric Inverse Monoids and Representation Theory" name="DC.title" />
  83. <meta content="FitzGerald, D.G." name="DC.creator" />
  84. <meta content="Leech, Jonathan" name="DC.creator" />
  85. <meta content="230105 Group Theory And Generalisations (Incl. Topological Groups And Lie Groups)" name="DC.subject" />
  86. <meta content="There is a substantial theory (modelled on permutation representations of groups) of representations of an
  87. inverse semigroup S in a symmetric inverse monoid I_X , that is, a monoid of partial one-to-one self-maps
  88. of a set X. The present paper describes the structure of a categorical dual I*_X to the symmetric inverse
  89. monoid and discusses representations of an inverse semigroup in this dual symmetric inverse monoid. It
  90. is shown how a representation of S by (full) selfmaps of a set X leads to dual pairs of representations
  91. in I_X and I*_X, and how a number of known representations arise as one or the other of these pairs.
  92. Conditions on S are described which ensure that representations of S preserve such infima or suprema as
  93. exist in the natural order of S. The categorical treatment allows the construction, from standard functors,
  94. of representations of S in certain other inverse algebras (that is, inverse monoids in which all finite infima
  95. exist). The paper concludes by distinguishing two subclasses of inverse algebras on the basis of their
  96. embedding properties." name="DC.description" />
  97. <meta content="1998" name="DC.date" />
  98. <meta content="Article" name="DC.type" />
  99. <meta content="PeerReviewed" name="DC.type" />
  100. <meta content="application/pdf" name="DC.format" />
  101. <meta content="http://eprints.utas.edu.au/1911/1/FL98.pdf" name="DC.identifier" />
  102. <meta content="http://www.austms.org.au/Publ/Jamsa/V64P3/pdf/e07.pdf" name="DC.relation" />
  103. <meta content="FitzGerald, D.G. and Leech, Jonathan (1998) Dual Symmetric Inverse Monoids and Representation Theory. Journal of the Australian Mathematical Society, Series A, 64 (3). pp. 345-367. ISSN 0263-6115" name="DC.identifier" />
  104. <meta content="http://eprints.utas.edu.au/1911/" name="DC.relation" />
  105. <link rel="alternate" href="http://eprints.utas.edu.au/cgi/export/1911/BibTeX/epprod-eprint-1911.bib" title="BibTeX" type="text/plain" />
  106. <link rel="alternate" href="http://eprints.utas.edu.au/cgi/export/1911/ContextObject/epprod-eprint-1911.xml" title="OpenURL ContextObject" type="text/xml" />
  107. <link rel="alternate" href="http://eprints.utas.edu.au/cgi/export/1911/ContextObject::Dissertation/epprod-eprint-1911.xml" title="OpenURL Dissertation" type="text/xml" />
  108. <link rel="alternate" href="http://eprints.utas.edu.au/cgi/export/1911/ContextObject::Journal/epprod-eprint-1911.xml" title="OpenURL Journal" type="text/xml" />
  109. <link rel="alternate" href="http://eprints.utas.edu.au/cgi/export/1911/DC/epprod-eprint-1911.txt" title="Dublin Core" type="text/plain" />
  110. <link rel="alternate" href="http://eprints.utas.edu.au/cgi/export/1911/DIDL/epprod-eprint-1911.xml" title="DIDL" type="text/xml" />
  111. <link rel="alternate" href="http://eprints.utas.edu.au/cgi/export/1911/EndNote/epprod-eprint-1911.enw" title="EndNote" type="text/plain" />
  112. <link rel="alternate" href="http://eprints.utas.edu.au/cgi/export/1911/HTML/epprod-eprint-1911.html" title="HTML Citation" type="text/html; charset=utf-8" />
  113. <link rel="alternate" href="http://eprints.utas.edu.au/cgi/export/1911/METS/epprod-eprint-1911.xml" title="METS" type="text/xml" />
  114. <link rel="alternate" href="http://eprints.utas.edu.au/cgi/export/1911/MODS/epprod-eprint-1911.xml" title="MODS" type="text/xml" />
  115. <link rel="alternate" href="http://eprints.utas.edu.au/cgi/export/1911/RIS/epprod-eprint-1911.ris" title="Reference Manager" type="text/plain" />
  116. <link rel="alternate" href="http://eprints.utas.edu.au/cgi/export/1911/Refer/epprod-eprint-1911.refer" title="Refer" type="text/plain" />
  117. <link rel="alternate" href="http://eprints.utas.edu.au/cgi/export/1911/Simple/epprod-eprint-1911text" title="Simple Metadata" type="text/plain" />
  118. <link rel="alternate" href="http://eprints.utas.edu.au/cgi/export/1911/Text/epprod-eprint-1911.txt" title="ASCII Citation" type="text/plain; charset=utf-8" />
  119. <link rel="alternate" href="http://eprints.utas.edu.au/cgi/export/1911/XML/epprod-eprint-1911.xml" title="EP3 XML" type="text/xml" />
  120.  
  121.   </head>
  122.   <body bgcolor="#ffffff" text="#000000" onLoad="loadRoutine(); MM_preloadImages('images/eprints/ePrints_banner_r5_c5_f2.gif','images/eprints/ePrints_banner_r5_c7_f2.gif','images/eprints/ePrints_banner_r5_c8_f2.gif','images/eprints/ePrints_banner_r5_c9_f2.gif','images/eprints/ePrints_banner_r5_c10_f2.gif','images/eprints/ePrints_banner_r5_c11_f2.gif','images/eprints/ePrints_banner_r6_c4_f2.gif')">
  123.     
  124.     <div class="ep_noprint"><noscript><style type="text/css">@import url(http://eprints.utas.edu.au/style/nojs.css);</style></noscript></div>
  125.  
  126.  
  127.  
  128.  
  129. <table width="795" border="0" cellspacing="0" cellpadding="0">
  130.   <tr>
  131.     <td><script language="JavaScript1.2">mmLoadMenus();</script>
  132.       <table border="0" cellpadding="0" cellspacing="0" width="795">
  133.         <!-- fwtable fwsrc="eprints_banner_final2.png" fwbase="ePrints_banner.gif" fwstyle="Dreamweaver" fwdocid = "1249563342" fwnested="0" -->
  134.         <tr>
  135.           <td><img src="/images/eprints/spacer.gif" width="32" height="1" border="0" alt="" /></td>
  136.           <td><img src="/images/eprints/spacer.gif" width="104" height="1" border="0" alt="" /></td>
  137.           <td><img src="/images/eprints/spacer.gif" width="44" height="1" border="0" alt="" /></td>
  138.           <td><img src="/images/eprints/spacer.gif" width="105" height="1" border="0" alt="" /></td>
  139.           <td><img src="/images/eprints/spacer.gif" width="41" height="1" border="0" alt="" /></td>
  140.           <td><img src="/images/eprints/spacer.gif" width="16" height="1" border="0" alt="" /></td>
  141.           <td><img src="/images/eprints/spacer.gif" width="68" height="1" border="0" alt="" /></td>
  142.           <td><img src="/images/eprints/spacer.gif" width="68" height="1" border="0" alt="" /></td>
  143.           <td><img src="/images/eprints/spacer.gif" width="68" height="1" border="0" alt="" /></td>
  144.           <td><img src="/images/eprints/spacer.gif" width="82" height="1" border="0" alt="" /></td>
  145.           <td><img src="/images/eprints/spacer.gif" width="69" height="1" border="0" alt="" /></td>
  146.           <td><img src="/images/eprints/spacer.gif" width="98" height="1" border="0" alt="" /></td>
  147.           <td><img src="/images/eprints/spacer.gif" width="1" height="1" border="0" alt="" /></td>
  148.         </tr>
  149.         <tr>
  150.           <td colspan="12"><img name="ePrints_banner_r1_c1" src="/images/eprints/ePrints_banner_r1_c1.gif" width="795" height="10" border="0" alt="" /></td>
  151.           <td><img src="/images/eprints/spacer.gif" width="1" height="10" border="0" alt="" /></td>
  152.         </tr>
  153.         <tr>
  154.           <td rowspan="6"><img name="ePrints_banner_r2_c1" src="/images/eprints/ePrints_banner_r2_c1.gif" width="32" height="118" border="0" alt="" /></td>
  155.           <td rowspan="5"><a href="http://www.utas.edu.au/"><img name="ePrints_banner_r2_c2" src="/images/eprints/ePrints_banner_r2_c2.gif" width="104" height="103" border="0" alt="" /></a></td>
  156.           <td colspan="10"><img name="ePrints_banner_r2_c3" src="/images/eprints/ePrints_banner_r2_c3.gif" width="659" height="41" border="0" alt="" /></td>
  157.           <td><img src="/images/eprints/spacer.gif" width="1" height="41" border="0" alt="" /></td>
  158.         </tr>
  159.         <tr>
  160.           <td colspan="3"><a href="http://eprints.utas.edu.au/"><img name="ePrints_banner_r3_c3" src="/images/eprints/ePrints_banner_r3_c3.gif" width="190" height="31" border="0" alt="" /></a></td>
  161.           <td rowspan="2" colspan="7"><img name="ePrints_banner_r3_c6" src="/images/eprints/ePrints_banner_r3_c6.gif" width="469" height="37" border="0" alt="" /></td>
  162.           <td><img src="/images/eprints/spacer.gif" width="1" height="31" border="0" alt="" /></td>
  163.         </tr>
  164.         <tr>
  165.           <td colspan="3"><img name="ePrints_banner_r4_c3" src="/images/eprints/ePrints_banner_r4_c3.gif" width="190" height="6" border="0" alt="" /></td>
  166.           <td><img src="/images/eprints/spacer.gif" width="1" height="6" border="0" alt="" /></td>
  167.         </tr>
  168.         <tr>
  169.           <td colspan="2"><img name="ePrints_banner_r5_c3" src="/images/eprints/ePrints_banner_r5_c3.gif" width="149" height="1" border="0" alt="" /></td>
  170.           <td rowspan="2" colspan="2"><a href="/information.html" onMouseOut="MM_swapImgRestore();MM_startTimeout()" onMouseOver="MM_showMenu(window.mm_menu_0821132634_0,0,25,null,'ePrints_banner_r5_c5');MM_swapImage('ePrints_banner_r5_c5','','/images/eprints/ePrints_banner_r5_c5_f2.gif',1);"><img name="ePrints_banner_r5_c5" src="/images/eprints/ePrints_banner_r5_c5.gif" width="57" height="25" border="0" alt="About" /></a></td>
  171.           <td rowspan="2"><a href="/view/" onMouseOut="MM_swapImgRestore();MM_startTimeout()" onMouseOver="MM_showMenu(window.mm_menu_0821133021_1,0,25,null,'ePrints_banner_r5_c7');MM_swapImage('ePrints_banner_r5_c7','','/images/eprints/ePrints_banner_r5_c7_f2.gif',1);"><img name="ePrints_banner_r5_c7" src="/images/eprints/ePrints_banner_r5_c7.gif" width="68" height="25" border="0" alt="Browse" /></a></td>
  172.           <td rowspan="2"><a href="/perl/search/simple" onMouseOut="MM_swapImgRestore();MM_startTimeout()" onMouseOver="MM_showMenu(window.mm_menu_0821133201_2,0,25,null,'ePrints_banner_r5_c8');MM_swapImage('ePrints_banner_r5_c8','','/images/eprints/ePrints_banner_r5_c8_f2.gif',1);"><img name="ePrints_banner_r5_c8" src="/images/eprints/ePrints_banner_r5_c8.gif" width="68" height="25" border="0" alt="Search" /></a></td>
  173.           <td rowspan="2"><a href="/perl/register" onMouseOut="MM_swapImgRestore();MM_startTimeout();" onMouseOver="MM_showMenu(window.mm_menu_1018171924_3,0,25,null,'ePrints_banner_r5_c9');MM_swapImage('ePrints_banner_r5_c9','','/images/eprints/ePrints_banner_r5_c9_f2.gif',1);"><img name="ePrints_banner_r5_c9" src="/images/eprints/ePrints_banner_r5_c9.gif" width="68" height="25" border="0" alt="register" /></a></td>
  174.           <td rowspan="2"><a href="/perl/users/home" onMouseOut="MM_swapImgRestore();MM_startTimeout()" onMouseOver="MM_showMenu(window.mm_menu_0821133422_4,0,25,null,'ePrints_banner_r5_c10');MM_swapImage('ePrints_banner_r5_c10','','/images/eprints/ePrints_banner_r5_c10_f2.gif',1);"><img name="ePrints_banner_r5_c10" src="/images/eprints/ePrints_banner_r5_c10.gif" width="82" height="25" border="0" alt="user area" /></a></td>
  175.           <td rowspan="2"><a href="/help/" onMouseOut="MM_swapImgRestore();MM_startTimeout()" onMouseOver="MM_showMenu(window.mm_menu_0821133514_5,0,25,null,'ePrints_banner_r5_c11');MM_swapImage('ePrints_banner_r5_c11','','/images/eprints/ePrints_banner_r5_c11_f2.gif',1);"><img name="ePrints_banner_r5_c11" src="/images/eprints/ePrints_banner_r5_c11.gif" width="69" height="25" border="0" alt="Help" /></a></td>
  176.           <td rowspan="3" colspan="4"><img name="ePrints_banner_r5_c12" src="/images/eprints/ePrints_banner_r5_c12.gif" width="98" height="40" border="0" alt="" /></td>
  177.           <td><img src="/images/eprints/spacer.gif" width="1" height="1" border="0" alt="" /></td>
  178.         </tr>
  179.         <tr>
  180.           <td rowspan="2"><img name="ePrints_banner_r6_c3" src="/images/eprints/ePrints_banner_r6_c3.gif" width="44" height="39" border="0" alt="ePrints home" /></td>
  181.           <td><a href="/" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('ePrints_banner_r6_c4','','/images/eprints/ePrints_banner_r6_c4_f2.gif',1);"><img name="ePrints_banner_r6_c4" src="/images/eprints/ePrints_banner_r6_c4.gif" width="105" height="24" border="0" alt="ePrints home" /></a></td>
  182.           <td><img src="/images/eprints/spacer.gif" width="1" height="24" border="0" alt="" /></td>
  183.         </tr>
  184.         <tr>
  185.           <td><img name="ePrints_banner_r7_c2" src="/images/eprints/ePrints_banner_r7_c2.gif" width="104" height="15" border="0" alt="" /></td>
  186.           <td colspan="8"><img name="ePrints_banner_r7_c4" src="/images/eprints/ePrints_banner_r7_c4.gif" width="517" height="15" border="0" alt="" /></td>
  187.           <td><img src="/images/eprints/spacer.gif" width="1" height="15" border="0" alt="" /></td>
  188.         </tr>
  189.       </table></td>
  190.   </tr>
  191.     <tr><td><table width="100%" style="font-size: 90%; border: solid 1px #ccc; padding: 3px"><tr>
  192.       <td align="left"><a href="http://eprints.utas.edu.au/cgi/users/home">Login</a> | <a href="http://eprints.utas.edu.au/cgi/register">Create Account</a></td>
  193.       <td align="right" style="white-space: nowrap">
  194.         <form method="get" accept-charset="utf-8" action="http://eprints.utas.edu.au/cgi/search" style="display:inline">
  195.           <input class="ep_tm_searchbarbox" size="20" type="text" name="q" />
  196.           <input class="ep_tm_searchbarbutton" value="Search" type="submit" name="_action_search" />
  197.           <input type="hidden" name="_order" value="bytitle" />
  198.           <input type="hidden" name="basic_srchtype" value="ALL" />
  199.           <input type="hidden" name="_satisfyall" value="ALL" />
  200.         </form>
  201.       </td>
  202.     </tr></table></td></tr>
  203.   <tr>
  204.     <td class="toplinks"><!-- InstanceBeginEditable name="content" -->
  205.  
  206.  
  207. <div align="center">
  208.   
  209.   <table width="720" class="ep_tm_main"><tr><td align="left">
  210.     <h1 class="ep_tm_pagetitle">Dual Symmetric Inverse Monoids and Representation Theory</h1>
  211.     <p style="margin-bottom: 1em" class="not_ep_block"><span class="person_name">FitzGerald, D.G.</span> and <span class="person_name">Leech, Jonathan</span> (1998) <xhtml:em>Dual Symmetric Inverse Monoids and Representation Theory.</xhtml:em> Journal of the Australian Mathematical Society, Series A, 64 (3). pp. 345-367. ISSN 0263-6115</p><p style="margin-bottom: 1em" class="not_ep_block"></p><table style="margin-bottom: 1em" class="not_ep_block"><tr><td valign="top" style="text-align:center"><a href="http://eprints.utas.edu.au/1911/1/FL98.pdf"><img alt="[img]" src="http://eprints.utas.edu.au/style/images/fileicons/application_pdf.png" border="0" class="ep_doc_icon" /></a></td><td valign="top"><a href="http://eprints.utas.edu.au/1911/1/FL98.pdf"><span class="ep_document_citation">PDF</span></a> - Full text restricted - Requires a PDF viewer<br />158Kb</td><td><form method="get" accept-charset="utf-8" action="http://eprints.utas.edu.au/cgi/request_doc"><input value="2405" name="docid" accept-charset="utf-8" type="hidden" /><div class=""><input value="Request a copy" name="_action_null" class="ep_form_action_button" onclick="return EPJS_button_pushed( '_action_null' )" type="submit" /> </div></form></td></tr></table><p style="margin-bottom: 1em" class="not_ep_block">Official URL: <a href="http://www.austms.org.au/Publ/Jamsa/V64P3/pdf/e07.pdf">http://www.austms.org.au/Publ/Jamsa/V64P3/pdf/e07.pdf</a></p><div class="not_ep_block"><h2>Abstract</h2><p style="padding-bottom: 16px; text-align: left; margin: 1em auto 0em auto">There is a substantial theory (modelled on permutation representations of groups) of representations of an&#13;
  212. inverse semigroup S in a symmetric inverse monoid I_X , that is, a monoid of partial one-to-one self-maps&#13;
  213. of a set X. The present paper describes the structure of a categorical dual I*_X to the symmetric inverse&#13;
  214. monoid and discusses representations of an inverse semigroup in this dual symmetric inverse monoid. It&#13;
  215. is shown how a representation of S by (full) selfmaps of a set X leads to dual pairs of representations&#13;
  216. in I_X and I*_X, and how a number of known representations arise as one or the other of these pairs.&#13;
  217. Conditions on S are described which ensure that representations of S preserve such infima or suprema as&#13;
  218. exist in the natural order of S. The categorical treatment allows the construction, from standard functors,&#13;
  219. of representations of S in certain other inverse algebras (that is, inverse monoids in which all finite infima&#13;
  220. exist). The paper concludes by distinguishing two subclasses of inverse algebras on the basis of their&#13;
  221. embedding properties.</p></div><table style="margin-bottom: 1em" border="0" cellpadding="3" class="not_ep_block"><tr><th valign="top" class="ep_row">Item Type:</th><td valign="top" class="ep_row">Article</td></tr><tr><th valign="top" class="ep_row">Keywords:</th><td valign="top" class="ep_row">dual symmetric inverse monoid, representations of inverse semigroups</td></tr><tr><th valign="top" class="ep_row">Subjects:</th><td valign="top" class="ep_row"><a href="http://eprints.utas.edu.au/view/subjects/230105.html">230000 Mathematical Sciences &gt; 230100 Mathematics &gt; 230105 Group Theory And Generalisations (Incl. Topological Groups And Lie Groups)</a></td></tr><tr><th valign="top" class="ep_row">Collections:</th><td valign="top" class="ep_row">UNSPECIFIED</td></tr><tr><th valign="top" class="ep_row">ID Code:</th><td valign="top" class="ep_row">1911</td></tr><tr><th valign="top" class="ep_row">Deposited By:</th><td valign="top" class="ep_row"><span class="ep_name_citation"><span class="person_name">Dr D. G. FitzGerald</span></span></td></tr><tr><th valign="top" class="ep_row">Deposited On:</th><td valign="top" class="ep_row">17 Sep 2007</td></tr><tr><th valign="top" class="ep_row">Last Modified:</th><td valign="top" class="ep_row">07 Feb 2008 12:22</td></tr><tr><th valign="top" class="ep_row">ePrint Statistics:</th><td valign="top" class="ep_row"><a target="ePrintStats" href="/es/index.php?action=show_detail_eprint;id=1911;">View statistics for this ePrint</a></td></tr></table><p align="right">Repository Staff Only: <a href="http://eprints.utas.edu.au/cgi/users/home?screen=EPrint::View&amp;eprintid=1911">item control page</a></p>
  222.   </td></tr></table>
  223. </div>
  224.  
  225.  
  226.  
  227.     <!-- InstanceEndEditable --></td>
  228.   </tr>
  229.   <tr>
  230.     <td><!-- #BeginLibraryItem "/Library/footer_eprints.lbi" -->
  231.     <table width="795" border="0" align="left" cellpadding="0" class="footer">
  232.   <tr valign="top">
  233. <td colspan="2"><div align="center"><a href="http://www.utas.edu.au">UTAS home</a> | <a href="http://www.utas.edu.au/library/">Library home</a> | <a href="/">ePrints home</a> | <a href="/contact.html">contact</a> | <a href="/information.html">about</a> | <a href="/view/">browse</a> | <a href="/perl/search/simple">search</a> | <a href="/perl/register">register</a> | <a href="/perl/users/home">user area</a> | <a href="/help/">help</a></div><br /></td>
  234. </tr>
  235. <tr><td colspan="2"><p><img src="/images/eprints/footerline.gif" width="100%" height="4" /></p></td></tr>
  236.       <tr valign="top">
  237.         <td width="68%" class="footer">Authorised by the University Librarian<br />
  238. © University of Tasmania ABN 30 764 374 782<br />
  239.       <a href="http://www.utas.edu.au/cricos/">CRICOS Provider Code 00586B</a> | <a href="http://www.utas.edu.au/copyright/copyright_disclaimers.html">Copyright &amp; Disclaimers</a> | <a href="http://www.utas.edu.au/accessibility/index.html">Accessibility</a> | <a href="http://eprints.utas.edu.au/feedback/">Site Feedback</a>  </td>
  240.         <td width="32%"><div align="right">
  241.             <p align="right" class="NoPrint"><a href="http://www.utas.edu.au/"><img src="http://www.utas.edu.au/shared/logos/unioftasstrip.gif" alt="University of Tasmania Home Page" width="260" height="16" border="0" align="right" /></a></p>
  242.             <p align="right" class="NoPrint"><a href="http://www.utas.edu.au/"><br />
  243.             </a></p>
  244.         </div></td>
  245.       </tr>
  246.       <tr valign="top">
  247.         <td><p>  </p></td>
  248.         <td><div align="right"><span class="NoPrint"><a href="http://www.eprints.org/software/"><img src="/images/eprintslogo.gif" alt="ePrints logo" width="77" height="29" border="0" align="bottom" /></a></span></div></td>
  249.       </tr>
  250.     </table>
  251.     <!-- #EndLibraryItem -->
  252.     <div align="center"></div></td>
  253.   </tr>
  254. </table>
  255.  
  256.   </body>
  257. </html>