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- W2039808432 abstract "Dans cet article, nous étudions la cohomologie (et l'homologie) de Hochschild H*(T,Λ) de l'algèbre T=(AM0B), où A et B sont deux algèbres unitaires, M est un A⊗Bo-module et Λ est un T-bimodule. En exprimant H*(T,Λ) comme cohomologie du complexe cône d'un morphisme dont la construction est simple, nous obtenons, non seulement de manière immédiate les suites exactes connues sur le sujet, mais de plus, sous l'hypothèse que M est projectif sur A (ou sur Bo), des suites exactes plus précises permettant de mieux comprendre HH*(T)=H*(T,T), en particulier lorsque Bo=EndA(M). Par exemple, nous obtenons un isomorphisme HH*(T)≅HH*(ϕ!), où ϕ:T→B est le morphisme canonique et ϕ! est l'algèbre introduite par Gerstenhaber et Shack pour l'étude de ses déformations [J. Algebra 95 (1985) 245–262]. We study the Hochschild cohomology (and homology) H*(T,Λ) of the triangular algebra T=(AM0B), with A and B unital algebras, M a A⊗Bo-module and Λ a T-bimodule. We describe H*(T,Λ) as the cohomology of the cone complex of a morphism, simple to construct. In this way we not only recover immediately the classical exact sequences of the field, but also, under the hypothesis that M is projective over A (or Bo), more precise exact sequences giving better insights for HH*(T)=H*(T,T), in particular when Bo=EndA(M). For instance, we get an isomorphism HH*(T)≅HH*(ϕ!), where ϕ:T→B is the canonical morphism and ϕ! is the algebra introduced by Gerstenhaber and Shack to study its deformations [J. Algebra 95 (1985) 245–262]." @default.
- W2039808432 created "2016-06-24" @default.
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- W2039808432 date "2004-12-01" @default.
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- W2039808432 title "Cohomologie de l'algèbre triangulaire et applications" @default.
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- W2039808432 doi "https://doi.org/10.1016/j.jalgebra.2004.02.036" @default.
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