Symmetric Self-Adjunctions: A Justification of Brauer’s Representation of Brauer’s Algebras
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چکیده
A classic result of representation theory is Brauer’s construction of a diagrammatical (geometrical) algebra whose matrix representation is a certain given matrix algebra, which is the commutating algebra of the enveloping algebra of the representation of the orthogonal group. The purpose of this paper is to provide a motivation for this result through the categorial notion of symmetric self-adjunction. Mathematics Subject Classification (2000): 14L24, 57M99, 20C99, 18A40
منابع مشابه
Symmetric Self-Adjunctions and Matrices
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 functors is satisfied. As in a previous paper, of which this is a companion, it is shown that such a symmetric self-adjunction...
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تاریخ انتشار 2005