PUBLICATIONS DE L'INSTITUT MATH\'EMATIQUE (BEOGRAD) (N.S.) EMIS ELibM Electronic Journals Publications de l'Institut Mathématique (Beograd)
Vol. 73(87), pp. 1-29 (2003)

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Kosta Do\v sen and Zoran Petri\'c

Matemati\v cki institut SANU, Beograd, Serbia

Abstract: This paper is a companion to another paper where it is shown that the multiplicative monoids of Temperley-Lieb algebras are isomorphic to monoids of endomorphisms in categories where an endofunctor is adjoint to itself. Such a self-adjunction underlies the orthogonal group case of Brauer's representation of the Brauer centralizer algebras. The present paper provides detailed proofs of results on the presentation of various monoids of diagrams by generators and relations, on which the other paper depends.

Keywords: tangles; monoids; Temperley-Lieb algebras; adjunction

Classification (MSC2000): 57M99; 20M50, 18A40

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