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Ideal Structure of the Kauffman and Related Monoids

journal contribution
posted on 2023-05-16, 18:17 authored by Lau, KW, Desmond FitzGeraldDesmond FitzGerald
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.

History

Publication title

Communications in Algebra

Volume

34

Issue

7

Pagination

2617-2629

ISSN

0092-7872

Department/School

School of Natural Sciences

Publisher

Taylor & Francis Inc

Place of publication

Philadelphia, USA

Repository Status

  • Restricted

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Expanding knowledge in the mathematical sciences

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