A. I. Generalov, “Hochschild cohomology of algebras of dihedral type. II. Local algebras”, Problems in the theory of representations of algebras and groups. Part 19, Zap. Nauchn. Sem. POMI, 375, POMI, St. Petersburg, 2010, 92–129; J. Math. Sci. (N. Y.), 171:3 (2010), 357

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Zapiski Nauchnykh Seminarov POMI, 2010, Volume 375, Pages 92–129 (Mi znsl3610)

This article is cited in 21 scientific papers (total in 21 papers)

Hochschild cohomology of algebras of dihedral type. II. Local algebras

A. I. Generalov

Saint-Petersburg State University, Saint-Petersburg, Russia

Full-text PDF (727 kB) Citations (21)

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Abstract: For local algebras which constitute a family of algebras of dihedral type, we calculate the Hochschild cohomology in the case where the base algebraically closed field has a characteristic different from 2. Furthermore, we give a description of the Hochschild cohomology algebra (in terms of generators and relations) for the local algebras under consideration. We use in the corresponding calculation a beforehand constructed bimodule resolution for these algebras. Bibl. – 19 titles.

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

Received: 13.01.2010

English version:
Journal of Mathematical Sciences (New York), 2010, Volume 171, Issue 3, Pages 357–379
DOI: https://doi.org/10.1007/s10958-010-0141-5

Bibliographic databases:

Document Type: Article

UDC: 512.5

Language: Russian

Citation: A. I. Generalov, “Hochschild cohomology of algebras of dihedral type. II. Local algebras”, Problems in the theory of representations of algebras and groups. Part 19, Zap. Nauchn. Sem. POMI, 375, POMI, St. Petersburg, 2010, 92–129; J. Math. Sci. (N. Y.), 171:3 (2010), 357–379

Citation in format AMSBIB

\Bibitem{Gen10}

\by A.~I.~Generalov

\paper Hochschild cohomology of algebras of dihedral type.~II. Local algebras

\inbook Problems in the theory of representations of algebras and groups. Part~19

\serial Zap. Nauchn. Sem. POMI

\yr 2010

\vol 375

\pages 92--129

\publ POMI

\publaddr St.~Petersburg

\mathnet{http://mi.mathnet.ru/znsl3610}

\transl

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

\yr 2010

\vol 171

\issue 3

\pages 357--379

\crossref{https://doi.org/10.1007/s10958-010-0141-5}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78649451595}

Linking options:

https://www.mathnet.ru/eng/znsl3610

https://www.mathnet.ru/eng/znsl/v375/p92

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 21 articles:

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