منابع مشابه
Hopf-Galois systems and Kashiwara algebras
This article is made up with two parts. In the first part, using a recent result of Schauenburg, one generalizes to the case when objects are faithfully flat over the ground ring, the full equivalence between the notions of Hopf-Galois objects and Hopf-Galois systems. In this last description, one gives explicitly an inverse for a Hopf-Galois object T together with its generalized antipode. In ...
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The notions of Galois and cleft extensions are generalized for coquasi-Hopf algebras. It is shown that such an extension over a coquasi-Hopf algebra is cleft if and only if it is Galois and has the normal basis property. A Schneider type theorem ([33]) is proven for coquasi-Hopf algebras with bijective antipode. As an application, we generalize Schauenburg’s bialgebroid construction for coquasi...
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In this paper we construct a cylindrical module A♮H for an Hcomodule algebra A, where the antipode of the Hopf algebra H is bijective. We show that the cyclic module associated to the diagonal of A♮H is isomorphic with the cyclic module of the crossed product algebra A ⋊H. This enables us to derive a spectral sequence for the cyclic homology of the crossed product algebra. We also construct a c...
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Hopf Galois theory expands the classical Galois theory by considering the Galois property in terms of the action of the group algebra k[G] on K/k and then replacing it by the action of a Hopf algebra. We review the case of separable extensions where the Hopf Galois property admits a group-theoretical formulation suitable for counting and classifying, and also to perform explicit computations an...
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Our goal in this paper is to define a version of Hochschild homology and cohomology suitable for a class of algebras admitting compatible actions of bialgebras, called “module algebras” (Definition 2.1). Our motivation lies in the following problem: for an algebra A which admits a module structure over an arbitrary bialgebra B compatible with its product structure, the Hochschild or the cyclic ...
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ژورنال
عنوان ژورنال: Mathematical surveys
سال: 2021
ISSN: ['0076-5376']
DOI: https://doi.org/10.1090/surv/260