A. I. Generalov, I. M. Zilberbord, D. B. Romanova, “Hochschild cohomology for algebras of dihedral type. V. The family $D(3\mathcal K)$ in characteristic different from 2”, Problems in the theory of representations of algebras and groups. Part 27, Zap. Nauchn. Sem. POMI, 430, POMI, St. Petersburg, 2014, 74–102; J. Math. Sci. (N. Y.), 219:3 (2016), 385

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Zapiski Nauchnykh Seminarov POMI, 2014, Volume 430, Pages 74–102 (Mi znsl6085)

This article is cited in 9 scientific papers (total in 9 papers)

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

St. Petersburg State University, St. Petersburg, Russia

Full-text PDF (296 kB) Citations (9)

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Abstract: We compute the Hochschild cohomology groups 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. In the calculation, we use the beforehand construction of the bimodule resolution for algebras from the family under discussion.

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

Received: 31.10.2014

English version:
Journal of Mathematical Sciences (New York), 2016, Volume 219, Issue 3, Pages 385–404
DOI: https://doi.org/10.1007/s10958-016-3115-4

Bibliographic databases:

Document Type: Article

UDC: 512.5

Language: Russian

Citation: A. I. Generalov, I. M. Zilberbord, D. B. Romanova, “Hochschild cohomology for algebras of dihedral type. V. The family $D(3\mathcal K)$ in characteristic different from 2”, Problems in the theory of representations of algebras and groups. Part 27, Zap. Nauchn. Sem. POMI, 430, POMI, St. Petersburg, 2014, 74–102; J. Math. Sci. (N. Y.), 219:3 (2016), 385–404

Citation in format AMSBIB

\Bibitem{GenZilRom14}

\by A.~I.~Generalov, I.~M.~Zilberbord, D.~B.~Romanova

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

\inbook Problems in the theory of representations of algebras and groups. Part~27

\serial Zap. Nauchn. Sem. POMI

\yr 2014

\vol 430

\pages 74--102

\publ POMI

\publaddr St.~Petersburg

\mathnet{http://mi.mathnet.ru/znsl6085}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3486764}

\transl

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

\yr 2016

\vol 219

\issue 3

\pages 385--404

\crossref{https://doi.org/10.1007/s10958-016-3115-4}

Linking options:

https://www.mathnet.ru/eng/znsl6085

https://www.mathnet.ru/eng/znsl/v430/p74

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

This publication is cited in the following 9 articles:

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