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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Hochschild cohomology of algebras of dihedral type, I: The family $ D(3\mathcal K)$ in characteristic $ 2$

Author: A. I. Generalov
Translated by: the author
Original publication: Algebra i Analiz, tom 16 (2004), nomer 6.
Journal: St. Petersburg Math. J. 16 (2005), 961-1012
MSC (2000): Primary 16E40
Published electronically: November 22, 2005
MathSciNet review: 2117449
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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 $ 2$. 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 $ q$.

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Additional Information

A. I. Generalov
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskiĭ Prospekt 28, Staryĭ Peterhof, St. Petersburg 198904, Russia

Keywords: Algebras of dihedral type, Hochschild cohomology
Received by editor(s): March 17, 2004
Published electronically: November 22, 2005
Article copyright: © Copyright 2005 American Mathematical Society

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