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Hochschild cohomology of algebras of dihedral type, I: The family $D(3\mathcal K)$ in characteristic

Author(s): A. I. Generalov
Translated by: the author
Original publication: Algebra i Analiz, tom 16 (2004), vypusk 6.
Journal: St. Petersburg Math. J. 16 (2005), 961-1012.
MSC (2000): Primary 16E40
Posted: November 22, 2005
MathSciNet review: 2117449
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Abstract | References | Similar articles | Additional information

Abstract: In terms of generators and defining relations, the Hochschild cohomology algebras are described for all algebras of dihedral type in the family $D(3\mathcal{K})$ over an algebraically closed field of characteristic . The results are applied to three other families of algebras of dihedral type, namely, $D(3\mathcal{A})_1$ , $D(3\mathcal{B})_1$ , and $D(3\mathcal{D})_1$ . 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 $\operatorname{PSL}(2,q)$ with odd .

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