Self-Adjunctions and Matrices

Details Self-Adjunctions and Matrices Self-Adjunctions and Matrices

2001-11-06

arxiv.org/abs/math/0111058v13

Mathematics

Geometric Topology

54 pages, minor corrections

Scientific paper

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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