About the naturality of Beattie's decomposition theorem with respect to a change of Hopf algebras

J. N. Alonso Alvarez; J. M. Fernández Vilaboa; R. González Rodríguez; E. Villanueva Novoa

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Displaying similar documents to “About the naturality of Beattie's decomposition theorem with respect to a change of Hopf algebras”

Inner actions and Galois $H$ -objects in a symmetric closed category

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On Galois $H$ -objects and invertible $H^{*}$ -modules

J. N. Alonso Alvarez, J. M. Fernández Vilaboa (2000)

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Twistings, crossed coproducts, and Hopf-Galois coextensions.

Caenepeel, S., Wang, Dingguo, Wang, Yanxin (2003)

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Galois H-objects with a normal basis in closed categories. A cohomological interpretation.

José N. Alonso Alvarez, José Manuel Fernández Vilaboa (1993)

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In this paper, for a cocommutative Hopf algebra H in a symmetric closed category C with basic object K, we get an isomorphism between the group of isomorphism classes of Galois H-objects with a normal basis and the second cohomology group H²(H,K) of H with coefficients in K. Using this result, we obtain a direct sum decomposition for the Brauer group of H-module Azumaya monoids with inner action: BM_inn(C,H) ≅ B(C) ⊕ H^2...

Hopf-Galois extensions for monoidal Hom-Hopf algebras

Yuanyuan Chen, Liangyun Zhang (2016)

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Hopf-Galois extensions for monoidal Hom-Hopf algebras are investigated. As the main result, Schneider's affineness theorem in the case of monoidal Hom-Hopf algebras is shown in terms of total integrals and Hopf-Galois extensions. In addition, we obtain an affineness criterion for relative Hom-Hopf modules which is associated with faithfully flat Hopf-Galois extensions of monoidal Hom-Hopf algebras.

Homotopy theory of Hopf Galois extensions

Christian Kassel, Hans-Jürgen Schneider (2005)

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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.

Smash (co)products and skew pairings.

José N. Alonso Alvarez, José Manuel Fernández Vilaboa, Ramón González Rodríguez (2001)

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Let τ be an invertible skew pairing on (B,H) where B and H are Hopf algebras in a symmetric monoidal category C with (co)equalizers. Assume that H is quasitriangular. Then we obtain a new algebra structure such that B is a Hopf algebra in the braided category γD and there exists a Hopf algebra isomorphism w: B ∞ H → B [×] H in C, where B ∞ H is a Hopf algebra with (co)algebra structure the smash (co)product and B [×] H is the Hopf algebra defined by Doi and Takeuchi. ...

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