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

Generalov, A.

doi:10.1090/S1061-0022-05-00886-1

Hochschild cohomology of algebras of dihedral type, I: The family $D(3\mathcal K)$ in characteristic $2$
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by A. I. Generalov
Translated by: the author

St. Petersburg Math. J. 16 (2005), 961-1012

DOI: https://doi.org/10.1090/S1061-0022-05-00886-1

Published electronically: November 22, 2005

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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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