Authors: Došen, Kosta 
Petrić, Zoran 
Title: Symmetric self-adjunctions and matrices
Journal: Algebra Colloquium
Volume: 19
Issue: SPL. ISS. 1
First page: 1051
Last page: 1082
Issue Date: 1-Dec-2012
ISSN: 1005-3867
DOI: 10.1142/S1005386712000855
It is shown that the multiplicative monoids of Brauer's centralizer algebras generated out of the basis are isomorphic to monoids of endomorphisms in categories where an endofunctor is adjoint to itself, and where, moreover, a kind of symmetry involving the self-adjoint functor is satisfied. As in a previous paper, of which this is a companion, it is shown that such a symmetric 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.
Keywords: adjunction | Brauer's centralizer algebras | matrix representation | symmetric groups
Publisher: World Scientific
Project: Representations of logical structures and formal languages and their application in computing 

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