Descent and Galois theory for Hopf categories
نویسندگان
چکیده
منابع مشابه
On Hopf-Galois extensions of linear categories
We continue the investigation of H-Galois extensions of linear categories, where H is a Hopf algebra. In our main result, the Theorem 2.2, we characterize this class of extensions in the case when H is finite dimensional. As an application, we prove a version of the Duality Theorem for crossed products with invertible cocycle. Introduction The duality theorems for actions and coactions originat...
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The relation between crossed product and H-Galois extension in braided tensor categories is established. It is shown that A = B#σH is a crossed product algebra if and only if the extension A/B is Galois, the inverse can of the canonical morphism can factors through object A⊗B A and A is isomorphic as left B-modules and right H-comodules to B⊗H in braided tensor categories. For the Yetter-Drinfe...
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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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In this paper we present a reformulation of the Galois correspondence theorem of Hopf Galois theory in terms of groups carrying farther the description of Greither and Pareigis. We prove that the class of Hopf Galois extensions for which the Galois correspondence is bijective is larger than the class of almost classically Galois extensions but not equal to the whole class. We show as well that ...
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We introduce the concept of homotopy equivalence for Hopf Galois extensions and make a systematic study of it. As an application we determine all H-Galois extensions up to homotopy equivalence in the case when H is a Drinfeld-Jimbo quantum group.
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ژورنال
عنوان ژورنال: Journal of Algebra and Its Applications
سال: 2018
ISSN: 0219-4988,1793-6829
DOI: 10.1142/s0219498818501207