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Zap. Nauchn. Sem. POMI, 2018, Volume 470, Pages 50–87 (Mi znsl6611)  

Hochschild cohomology of algebras of dihedral type. VIII. The Hochschild cohomology algebra for the family $D(2\mathcal B)(k,s,0)$ in characteristic $2$

A. I. Generalov, N. Yu. Kosovskaia

St. Petersburg State University, St. Petersburg, Russia

Abstract: We describe the Hochschild cohomology algebra for algebras of dihedral type in the subfamily of the family $D(2\mathcal B)$, for which the parameter $c$ is equal to $0$. In the calculation of multiplication in this cohomology algebra, we use the minimal bimodule projective resolution for the algebras under consideration that was constructed in the previous paper of the authors. The obtained results allow us to describe the Hochschild cohomology algebra also for algebras in the family $D(2\mathcal A)$ for which $c=0$.

Key words and phrases: Hochschild cohomology algebra, algebras of dihedral type, bimodule resolution.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-01-00258


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Document Type: Article
UDC: 512.5
Received: 08.10.2018

Citation: A. I. Generalov, N. Yu. Kosovskaia, “Hochschild cohomology of algebras of dihedral type. VIII. The Hochschild cohomology algebra for the family $D(2\mathcal B)(k,s,0)$ in characteristic $2$”, Problems in the theory of representations of algebras and groups. Part 33, Zap. Nauchn. Sem. POMI, 470, POMI, St. Petersburg, 2018, 50–87

Citation in format AMSBIB
\Bibitem{GenKos18}
\by A.~I.~Generalov, N.~Yu.~Kosovskaia
\paper Hochschild cohomology of algebras of dihedral type.~VIII. The Hochschild cohomology algebra for the family $D(2\mathcal B)(k,s,0)$ in characteristic~$2$
\inbook Problems in the theory of representations of algebras and groups. Part~33
\serial Zap. Nauchn. Sem. POMI
\yr 2018
\vol 470
\pages 50--87
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6611}


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