eCite Digital Repository

Ideal Structure of the Kauffman and Related Monoids


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


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
UTAS Author:FitzGerald, DG (Dr Des FitzGerald)
ID Code:41161
Year Published:2006
Web of Science® Times Cited:24
Deposited By:Mathematics
Deposited On:2006-08-01
Last Modified:2010-06-10

Repository Staff Only: item control page