Symmetric Self-adjunctions and Matrices
نویسندگان
چکیده
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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It is shown that the multiplicative monoids of Temperley-Lieb algebras 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. Thereby one obtains a representation of braid groups in matrices, which,...
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In a recent paper Calderbank, Rains, Shor and Sloane [1] described a method of constructing quantum-error-correcting codes from ordinary binary or quaternary codes that are selforthogonal with respect to a certain inner product. We use this relation to show that a class of binary formally self-dual codes defined by symmetric matrices give rise to quantum codes with error-correcting capacity pro...
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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-ad...
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ژورنال
عنوان ژورنال: Algebra Colloquium
سال: 2012
ISSN: 1005-3867,0219-1733
DOI: 10.1142/s1005386712000855