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  27. <meta content="The generators of the Temperley-Lieb algebra generate a monoid with an appealing geometric representation. It has been much studied, notably by Louis Kauffman. Borisavljevic, Dosen, and Petric gave a complete proof of its abstract presentation by generators and relations, and suggested the name 'Kauffman monoid'. We bring the theory of semigroups to the study of a certain finite homomorphic image of the Kauffman monoid. We show the homomorphic image (the Jones monoid) to be a combinatorial and regular *-semigroup with linearly ordered ideals. The Kauffman monoid is explicitly described in terms of the Jones monoid and a purely combinatorial numerical function. We use this to describe the ideal structure of the Kauffman monoid
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  39. <meta content="Borisavljevic, M.; Dosen, K.; Petric, Z. Kauffman monoids. J. Knot Theory Ramifications 2002, 11, 127--143.
  40. Dosen, K.; Petric, Z. Self-adjunctions and matrices. J. Pure Appl. Algebra 2003, 184, 7--39.
  41. Howie, J. M. Fundamentals of semigroup theory; Oxford University Press: Oxford, 1995.
  42. Jones., V. F. R. Index for subfactors. Invent. Math. 1983, 72, 1--25.
  43. Kauffman, L. H. An invariant of regular isotopy. Trans. Amer. Math. Soc. 1990, 318, 417--471.
  44. Nordahl, T. E.; Scheiblich, H. E. Regular *-semigroups. Semigroup Forum 1978, 16, 369--377.
  45. Temperley, H. N. V.; Lieb, E. H. Relations between the `percolation' and `colouring' problem and other graph-theoretic problems associated with regular planar lattices: some exact results for the `percolation' problem. Proc. Roy. Soc. Lond. A 1971, 322, 251--280." name="eprints.referencetext" />
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  53. <meta content="The generators of the Temperley-Lieb algebra generate a monoid with an appealing geometric representation. It has been much studied, notably by Louis Kauffman. Borisavljevic, Dosen, and Petric gave a complete proof of its abstract presentation by generators and relations, and suggested the name 'Kauffman monoid'. We bring the theory of semigroups to the study of a certain finite homomorphic image of the Kauffman monoid. We show the homomorphic image (the Jones monoid) to be a combinatorial and regular *-semigroup with linearly ordered ideals. The Kauffman monoid is explicitly described in terms of the Jones monoid and a purely combinatorial numerical function. We use this to describe the ideal structure of the Kauffman monoid
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  168.     <h1 class="ep_tm_pagetitle">Ideal structure of the Kauffman and related monoids</h1>
  169.     <p style="margin-bottom: 1em" class="not_ep_block"><span class="person_name">Lau, Kwok Wai</span> and <span class="person_name">FitzGerald, D.G.</span> (2006) <xhtml:em>Ideal structure of the Kauffman and related monoids.</xhtml:em> Communications in Algebra, 34 . pp. 2617-2629. ISSN 0092-7872</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 onmouseover="EPJS_ShowPreview( event, 'doc_preview_1810' );" href="http://eprints.utas.edu.au/1407/1/IDEAL_Jones.pdf" onmouseout="EPJS_HidePreview( event, 'doc_preview_1810' );"><img alt="[img]" src="http://eprints.utas.edu.au/style/images/fileicons/application_pdf.png" class="ep_doc_icon" border="0" /></a><div class="ep_preview" id="doc_preview_1810"><table><tr><td><img alt="" src="http://eprints.utas.edu.au/1407/thumbnails/1/preview.png" class="ep_preview_image" border="0" /><div class="ep_preview_title">Preview</div></td></tr></table></div></td><td valign="top"><a href="http://eprints.utas.edu.au/1407/1/IDEAL_Jones.pdf"><span class="ep_document_citation">PDF (Author Version)</span></a> - Requires a PDF viewer<br />172Kb</td></tr></table><p style="margin-bottom: 1em" class="not_ep_block">Official URL: <a href="http://dx.doi.org/10.1080/00927870600651414">http://dx.doi.org/10.1080/00927870600651414</a></p><div class="not_ep_block"><h2>Abstract</h2><p style="padding-bottom: 16px; text-align: left; margin: 1em auto 0em auto">The generators of the Temperley-Lieb algebra generate a monoid with an appealing geometric representation. It has been much studied, notably by Louis Kauffman. Borisavljevic, Dosen, and Petric gave a complete proof of its abstract presentation by generators and relations, and suggested the name 'Kauffman monoid'. We bring the theory of semigroups to the study of a certain finite homomorphic image of the Kauffman monoid. We show the homomorphic image (the Jones monoid) to be a combinatorial and regular *-semigroup with linearly ordered ideals. The Kauffman monoid is explicitly described in terms of the Jones monoid and a purely combinatorial numerical function. We use this to describe the ideal structure of the Kauffman monoid&#13;
  170. and two other of its homomorphic images.</p></div><table style="margin-bottom: 1em" cellpadding="3" class="not_ep_block" border="0"><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">Additional Information:</th><td valign="top" class="ep_row">The definitive version at Taylor and Francis Publishing</td></tr><tr><th valign="top" class="ep_row">Keywords:</th><td valign="top" class="ep_row">Ideal structure; Kauffman monoid.</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">ID Code:</th><td valign="top" class="ep_row">1407</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">19 Jul 2007</td></tr><tr><th valign="top" class="ep_row">Last Modified:</th><td valign="top" class="ep_row">09 Jan 2008 02:30</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=1407;">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=1407">item control page</a></p>
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