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- W2074961943 abstract "Etant donné le produit croisé B = G ×αA d'une algèbre A par un groupe d'automorphismes G, et un B-bimodule X, on construit une filtration du complexe standard Hom ( ⊗ *B, X) calculant la cohomologie de Hochschild H*(B, X); on montre ensuite que la suite spectrale associée à cette filtration vérifie Ep, q2 = Hp(G, Hq(A, X)). Ceci généralise la “méthode directe” utilisée par Hochschild et Serre (1953) dans le cas des extensions de groupes. On applique cela à certains automorphismes des tores Td: on prend pour G le groupe Z, pour A — l'algèbre des polynômes trigonométriques sur Td, et on construit des bases des divers espaces Hn(B, B) au sein du complexe standard Hom ( ⊗ *B, B). Given the crossed product B = G ×αA of an algebra A by a group of automorphisms G, and a B-bimodule X, we construct a filtration of the standard complex Hom ( ⊗ *B, X) which computes the Hochschild cohomology H*(B, X): then we show that the associated spectral sequence satisfies Ep, q2 = Hp(G, Hq(A, X)). This generalizes the “direct method” used by Hochschild and Serre (1953) in the case of a group extension. We apply this to certain automorphisms of the tori Td where G is the group Z and A is the algebra of trigonometric polynomials on Td, and we construct bases of the spaces Hn(B, B) inside the standard complex Hom ( ⊗ *B, B)." @default.
- W2074961943 created "2016-06-24" @default.
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- W2074961943 date "2001-01-01" @default.
- W2074961943 modified "2023-09-30" @default.
- W2074961943 title "Suites spectrales à la Hochschild–Serre pour les produits croisés d'algèbres et de groupes" @default.
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- W2074961943 doi "https://doi.org/10.1006/jabr.2000.8498" @default.
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