The Picard crossed module of a braided tensor category
نویسندگان
چکیده
منابع مشابه
The category of generalized crossed modules
In the definition of a crossed module $(T,G,rho)$, the actions of the group $T$ and $G$ on themselves are given by conjugation. In this paper, we consider these actions to be arbitrary and thus generalize the concept of ordinary crossed module. Therefore, we get the category ${bf GCM}$, of all generalized crossed modules and generalized crossed module morphisms between them, and investigate som...
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For a Hopf algebra H over a commutative ring k and a left H-module V, the tensor endofunctors V k - and - kV are left adjoint to some kinds of Hom-endofunctors of _HM. The units and counits of these adjunctions are formally trivial as in the classical case.The category of (bi-) modules over a quasi-Hopf algebra is monoidal and some generalized versions of Hom-tensor relations have been st...
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We show that the braided tensor product algebra A1⊗A2 of two module algebras A1,A2 of a quasitriangular Hopf algebraH is equal to the ordinary tensor product algebra of A1 with a subalgebra of A1⊗A2 isomorphic to A2, provided there exists a realization of H within A1. In other words, under this assumption we construct a transformation of generators which ‘decouples’ A1,A2 (i.e. makes them commu...
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We briefly report on our result [9] that the braided tensor product algebra of two module algebras A1,A2 of a quasitriangular Hopf algebra H is equal to the ordinary tensor product algebra of A1 with a subalgebra isomorphic to A2 and commuting with A1, provided there exists a realization of H within A1. As applications of the theorem we consider the braided tensor product algebras of two or mor...
متن کاملThe non-abelian tensor product of normal crossed submodules of groups
In this article, the notions of non-abelian tensor and exterior products of two normal crossed submodules of a given crossed module of groups are introduced and some of their basic properties are established. In particular, we investigate some common properties between normal crossed modules and their tensor products, and present some bounds on the nilpotency class and solvability length of the...
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ژورنال
عنوان ژورنال: Algebra & Number Theory
سال: 2013
ISSN: 1944-7833,1937-0652
DOI: 10.2140/ant.2013.7.1365