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Ideal structure of the Kauffman and related monoids
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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
and two other of its homomorphic images.
|Keywords:||Ideal structure; Kauffman monoid.|
|Journal or Publication Title:||Communications in Algebra|
|Page Range:||pp. 2617-2629|
|Identification Number - DOI:||10.1080/00927870600651414|
The definitive version at Taylor and Francis Publishing
|Date Deposited:||19 Jul 2007|
|Last Modified:||18 Nov 2014 03:19|
|Item Statistics:||View statistics for this item|
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