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

Título inglés Galois H-objects with a normal basis in closed categories. A cohomological interpretation.
Título español H-objetos de Galois con una base normal en categorías cerradas. Interpretación cohomológica.
Autor/es Alonso Alvarez, José N. ; Fernández Vilaboa, José Manuel
Organización Dep. Mat. Univ. Vigo, Vigo (Pontevedra), España;Dep. Alx. Univ. Santiago de Compostela, Santiago de Compostela (La Coruña), España
Revista 0214-1493
Publicación 1993, 37 (2): 271-284, 23 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés 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.
Clasificación UNESCO 120100
Palabras clave español Algebra de Hopf ; Grupo de Galois ; Grupo de Brauer ; Categorías cerradas ; Cohomología
Código MathReviews MR1249231
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