IDEAL_Jones.pdf (172.12 kB)
Ideal structure of the Kauffman and related monoids
journal contribution
posted on 2023-05-25, 23:39 authored by Lau, KW, FitzGerald, DGThe 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.
History
Publication title
Communications in AlgebraVolume
34Pagination
2617-2629ISSN
0092-7872Department/School
Menzies Research InstitutePublication status
- Published
Rights statement
The definitive version at Taylor and Francis PublishingRepository Status
- Open