Self-Adjunctions and Matrices
Geometric Topology
2008-07-10 v9
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.
Cite
@article{arxiv.math/0111058,
title = {Self-Adjunctions and Matrices},
author = {K. Dosen and Z. Petric},
journal= {arXiv preprint arXiv:math/0111058},
year = {2008}
}
Comments
54 pages, minor corrections