منابع مشابه
The Quantum Double as a Hopf Algebra
In the last lecture we have learned that the category of modules over a braided Hopf algebra H is a braided monoidal category. A braided Hopf algebra is a rather sophisticated algebraic object, it is not easy to give interesting nontrivial examples. In this text we develop a theory that will lead to a concrete recipe which produces a nontrivial braided Hopf algebra D(A) (called Drinfeld’s quant...
متن کاملThe bar construction as a Hopf algebra
Recall that deformations of Hochschild cochains are controlled by a homotopy Baues algebra (B∞-algebra) structure, and therefore a homotopy Gerstenhaber algebra structure on the Hochschild complex. The purpose of the present article is twofold. We first answer one of the classical questions addressed to algebraic topology. Namely, we construct a B∞-algebra structure on singular cochain complexe...
متن کاملGorenstein global dimensions for Hopf algebra actions
Let $H$ be a Hopf algebra and $A$ an $H$-bimodule algebra. In this paper, we investigate Gorenstein global dimensions for Hopf algebras and twisted smash product algebras $Astar H$. Results from the literature are generalized.
متن کاملAdjunctions between Hom and Tensor as endofunctors of (bi-) module category of comodule algebras over a quasi-Hopf algebra.
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...
متن کاملHopf Algebra Extensions of Monogenic Hopf Algebras
William M. Singer has described a cohomology theory of connected Hopf algebras which classifies extensions of a cocommutative Hopf algebra by a commutative Hopf algebra in much the same way as the cohomology of groups classifies extensions of a group by an abelian group. We compute these cohomology groups for monogenic Hopf algebras, construct an action of the base ring on the cohomology groups...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1977
ISSN: 0022-4049
DOI: 10.1016/0022-4049(77)90022-6