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Ideal Structure of the Kauffman and Related Monoids

Citation

Lau, KW and FitzGerald, DG, Ideal Structure of the Kauffman and Related Monoids, Communications in Algebra, 34, (7) pp. 2617-2629. ISSN 0092-7872 (2006) [Refereed Article]

DOI: doi:10.1080/00927870600651414

Abstract

The generators of the Temperley-Lieb algebra generate a monoid with an appealing geometric representation. It has been much studied, notably by Louis Kauffman. Borisavljević, Doen, and Petrić 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 Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Pure Mathematics
Research Field:Group Theory and Generalisations
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:FitzGerald, DG (Dr Des FitzGerald)
ID Code:41161
Year Published:2006
Web of Science® Times Cited:13
Deposited By:Mathematics
Deposited On:2006-08-01
Last Modified:2010-06-10
Downloads:0

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