Ideal structure of the Kau¤man and related monoids
نویسندگان
چکیده
The generators of the Temperley-Lieb algebra generate a monoid with an appealing geometric representation. It has been much studied, notably by Louis Kau¤man. Borisavljevíc, Doen and Petríc gave a complete proof of its abstract presentation by generators and relations, and suggested the name Kau¤man monoid. We bring the theory of semigroups to the study of a certain nite homomorphic image of the Kau¤man monoid. We show the homomorphic image (the Jones monoid) to be a combinatorial and regular *-semigroup with linearly ordered ideals. The Kau¤man 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 Kau¤man monoid and two other of its homomorphic images. Key Words: Kau¤man monoid, ideal structure 2000 Mathematics Subject Classi cation: 20M20
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