Hochschild Cohomology of Algebras of Dihedral Type, I: the Family D(3k) in Characteristic 2
نویسنده
چکیده
In terms of generators and defining relations, the Hochschild cohomology algebras are described for all algebras of dihedral type in the family D(3K) over an algebraically closed field of characteristic 2. The results are applied to three other families of algebras of dihedral type, namely, D(3A)1, D(3B)1, and D(3D)1. As a corollary, a description is obtained for the Hochschild cohomology algebra for blocks with dihedral defect group and three simple modules; in particular, this applies to principal blocks of the groups PSL(2, q) with odd q. Introduction Let R be a finite-dimensional algebra over a field K, and let Λ = R e = R ⊗K R be its enveloping algebra. Then the nth Hochschild cohomology group of the algebra R with coefficients in an R-bimodule M is defined as follows: HH(R,M) = ExtΛ(R,M). If M = R, we use the notation HH(R) = HH(R,R). On the vector space HH∗(R) = ⊕
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