Galois H-objects with a normal basis in closed categories: a cohomological interpretation
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Autores: José N. Alonso Álvarez
, José Manuel Fernández Vilaboa
- Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 37, Nº 2, 1993, págs. 271-284
- Idioma: inglés
- DOI: 10.5565/publmat_37293_03
- Títulos paralelos:
- H-objetos de Galois con una base normal en categorías cerradas: interpretación cohomológica
- Enlaces
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Resumen
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:
BMinn(C,H) @ B(C) Å H2(H,K) In particular, if C is the symmetric closed category of C-modules with K a field, H2(H,K) is the second cohomology group introduced by Sweedler in [21]. Moreover, if H is a finitely generated projective, commutative and cocommutative Hopf algebra over a commutative ring with unit K, then the above decomposition theorem is the one obtained by Beattie [5] for the Brauer group of H-module algebras.
