Self-Adjunctions and Matrices

K. Dosen; Z. Petric

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arXiv · math/0111058

Self-Adjunctions and Matrices

K. Dosen·Z. Petric

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Abstract

It is shown that the multiplicative monoids of Temperley-Lieb algebras generated out of the basis 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 the Brauer representation of the Brauer centralizer algebra.

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BibTeX RIS

K. Dosen, Z. Petric. 2008-07-10. Self-Adjunctions and Matrices. https://arxiv.org/abs/math/0111058

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