A. I. Generalov, M. A. Kachalova, P. A. Mostovskij, “Hochschild cohomology of algebras of dihedral type. IX. The Hochschild cohomology algebra for the family $D(3\mathcal K)$ in characteristic different from $2$”, Problems in the theory of representations of algebras and groups. Part 38, Zap. Nauchn. Sem. POMI, 513, POMI, St. Petersburg, 2022, 30–56; J. Math. Sci. (N. Y.), 288:3 (2025), 284

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Zapiski Nauchnykh Seminarov POMI, 2022, Volume 513, Pages 30–56 (Mi znsl7228)

This article is cited in 4 scientific papers (total in 4 papers)

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^a, M. A. Kachalova^b, P. A. Mostovskij^c

^a Saint Petersburg State University
^b Yandex company, Moscow
^c Saint-Petersburg State University, Department of Mathematics and Computer Science

Full-text PDF (265 kB) Citations (4) English version article

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Abstract: The Hochschild cohomology ring for algebras of dihedral type which form the family $D(3\mathcal K)$ (from the famous K. Erdmann's classification) over an algebraically closed field with characteristic different from $2$ is described in terms of generators and relations.

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

Funding agency	Grant number
Russian Foundation for Basic Research	20-01-00030

Received: 10.04.2022

English version:
Journal of Mathematical Sciences (New York), 2025, Volume 288, Issue 3, Pages 284–304
DOI: https://doi.org/10.1007/s10958-025-07698-0

Bibliographic databases:

Document Type: Article

UDC: 512.5

Language: Russian

Citation: A. I. Generalov, M. A. Kachalova, P. A. Mostovskij, “Hochschild cohomology of algebras of dihedral type. IX. The Hochschild cohomology algebra for the family $D(3\mathcal K)$ in characteristic different from $2$”, Problems in the theory of representations of algebras and groups. Part 38, Zap. Nauchn. Sem. POMI, 513, POMI, St. Petersburg, 2022, 30–56; J. Math. Sci. (N. Y.), 288:3 (2025), 284–304

Citation in format AMSBIB

\Bibitem{GenKacMos22}

\by A.~I.~Generalov, M.~A.~Kachalova, P.~A.~Mostovskij

\paper Hochschild cohomology of algebras of dihedral type. IX. The Hochschild cohomology algebra for the family $D(3\mathcal K)$ in characteristic different from~$2$

\inbook Problems in the theory of representations of algebras and groups. Part~38

\serial Zap. Nauchn. Sem. POMI

\yr 2022

\vol 513

\pages 30--56

\publ POMI

\publaddr St.~Petersburg

\mathnet{http://mi.mathnet.ru/znsl7228}

\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4508370}

\transl

\jour J. Math. Sci. (N. Y.)

\yr 2025

\vol 288

\issue 3

\pages 284--304

\crossref{https://doi.org/10.1007/s10958-025-07698-0}

Linking options:

https://www.mathnet.ru/eng/znsl7228

https://www.mathnet.ru/eng/znsl/v513/p30

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 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

This publication is cited in the following 4 articles:

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