A. I. Generalov, I. M. Zilberbord, V. A. Rogov, “Hochschild cohomology for algebras of dihedral type. X. Exceptional local algebras”, Problems in the theory of representations of algebras and groups. Part 39, Zap. Nauchn. Sem. POMI, 522, POMI, St. Petersburg, 2023, 60

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Zapiski Nauchnykh Seminarov POMI, 2023, Volume 522, Pages 60–83 (Mi znsl7336)

Hochschild cohomology for algebras of dihedral type. X. Exceptional local algebras

A. I. Generalov^a, I. M. Zilberbord^a, V. A. Rogov

^a Saint Petersburg State University

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Abstract: The Hochschild cohomology groups are computed for “exceptional” local algebras of dihedral type (from the famous K. Erdmann's classification) which appear when the base field has characteristic 2. In the calculation, we use the beforehand construction of the bimodule resolution for the algebras in question.

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

Funding agency	Grant number
Russian Science Foundation	22-71-10001

Received: 04.05.2023

Document Type: Article

UDC: 512.5

Language: Russian

Citation: A. I. Generalov, I. M. Zilberbord, V. A. Rogov, “Hochschild cohomology for algebras of dihedral type. X. Exceptional local algebras”, Problems in the theory of representations of algebras and groups. Part 39, Zap. Nauchn. Sem. POMI, 522, POMI, St. Petersburg, 2023, 60–83

Citation in format AMSBIB

\Bibitem{GenZilRog23}

\by A.~I.~Generalov, I.~M.~Zilberbord, V.~A.~Rogov

\paper Hochschild cohomology for algebras of dihedral type. X. Exceptional local algebras

\inbook Problems in the theory of representations of algebras and groups. Part~39

\serial Zap. Nauchn. Sem. POMI

\yr 2023

\vol 522

\pages 60--83

\publ POMI

\publaddr St.~Petersburg

\mathnet{http://mi.mathnet.ru/znsl7336}

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https://www.mathnet.ru/eng/znsl7336

https://www.mathnet.ru/eng/znsl/v522/p60

Cycle of papers

Hochschild cohomologies of dihedral type algebras, I: $D(3\mathcal K)$ series in characteristic 2
A. I. Generalov
Algebra i Analiz, 2004, 16:6, 53–122
Hochschild cohomology of algebras of dihedral type. II. Local algebras
A. I. Generalov
Zap. Nauchn. Sem. POMI, 2010, 375, 92–129
Hochschild cohomology for algebras of dihedral type. IV. The family $D(2\mathcal B)(k,s,0)$
A. I. Generalov, N. Yu. Kosovskaia
Zap. Nauchn. Sem. POMI, 2014, 423, 67–104
Hochschild cohomology for algebras of dihedral type. V. The family $D(3\mathcal K)$ in characteristic different from 2
A. I. Generalov, I. M. Zilberbord, D. B. Romanova
Zap. Nauchn. Sem. POMI, 2014, 430, 74–102
Hochschild cohomology for algebras of dihedral type. VI. The family $D(2\mathcal B)(k,s,1)$
A. I. Generalov, D. B. Romanova
Algebra i Analiz, 2015, 27:6, 89–116
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
Zap. Nauchn. Sem. POMI, 2018, 470, 50–87
Hochschild cohomology of algebras of dihedral type. IX. The Hochschild cohomology algebra for the family $D(3\mathcal K)$ in characteristic different from $2$
A. I. Generalov, M. A. Kachalova, P. A. Mostovskij
Zap. Nauchn. Sem. POMI, 2022, 513, 30–56
Hochschild cohomology for algebras of dihedral type. X. Exceptional local algebras
A. I. Generalov, I. M. Zilberbord, V. A. Rogov
Zap. Nauchn. Sem. POMI, 2023, 522, 60–83
Hochschild cohomology of algebras of dihedral type. XI. Cohomology algebra for a family of exceptional algebras
A. I. Generalov
Zap. Nauchn. Sem. POMI, 2024, 531, 71–100
Hochschild cohomology of algebras of dihedral type. XII. Cohomology algebra for a family of exceptional algebras with two simple modules
A. I. Generalov
Zap. Nauchn. Sem. POMI, 2024, 538, 5–44

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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