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Ideal structure of the Kauffman and related monoids


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Lau, KW and FitzGerald, DG 2006 , 'Ideal structure of the Kauffman and related monoids' , Communications in Algebra, vol. 34 , pp. 2617-2629 , doi: 10.1080/00927870600651414.

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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.

Item Type: Article
Authors/Creators:Lau, KW and FitzGerald, DG
Keywords: Ideal structure; Kauffman monoid.
Journal or Publication Title: Communications in Algebra
ISSN: 0092-7872
DOI / ID Number: 10.1080/00927870600651414
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The definitive version at Taylor and Francis Publishing

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