Authors: Došen, Kosta 
Petrić, Zoran 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Self-adjunctions and matrices
Journal: Journal of Pure and Applied Algebra
Volume: 184
Issue: 1
First page: 7
Last page: 39
Issue Date: 1-Oct-2003
Rank: M22
ISSN: 0022-4049
DOI: 10.1016/S0022-4049(03)00084-7
Abstract: 
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 is found in a category whose arrows are matrices, and the functor adjoint to itself is based on the Kronecker product of matrices. This self-adjunction underlies the orthogonal group case of Brauer's representation of the Brauer centralizer algebras.
Publisher: Elsevier
Project: Ministry of Science, Technology and Development of Serbia, grant 1630 (Representation of proofs with applications, classification of structures and infinite combinatorics)

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