Hochschild Cohomology of Algebras of Quaternion Type, I: Generalized Quaternion Groups
نویسنده
چکیده
In terms of generators and defining relations, a description is given of the Hochschild cohomology algebra for one of the series of local algebras of quaternion type. As a corollary, the Hochschild cohomology algebra is described for the group algebras of generalized quaternion groups over algebraically closed fields of characteristic 2. Introduction Let R be a finite-dimensional algebra over a field K, let Λ = R e = R ⊗K R be its enveloping algebra, and let HH(R) = ExtΛ(R,R) be the nth Hochschild cohomology group of the algebra R (with coefficients in the R-bimodule R). On the vector space HH∗(R) = ⊕
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