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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