A. I. Generalov, I. M. Zilberbord, “Hochschild cohomology for algebras of semidihedral type. V. The family $SD(3\mathcal K)$”, Problems in the theory of representations of algebras and groups. Part 28, Zap. Nauchn. Sem. POMI, 435, POMI, St. Petersburg, 2015, 5–32; J. Math. Sci. (N. Y.), 219:4 (2016), 493

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Zapiski Nauchnykh Seminarov POMI, 2015, Volume 435, Pages 5–32 (Mi znsl6148)

This article is cited in 8 scientific papers (total in 8 papers)

Hochschild cohomology for algebras of semidihedral type. V. The family

S D (3 K)

$SD(3\mathcal K)$

A. I. Generalov, I. M. Zilberbord

St. Petersburg State University, St. Petersburg, Russia

Full-text PDF (298 kB) Citations (8)

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Abstract: We compute the Hochschild cohomology groups for algebras of semidihedral type from the family

S D (3 K)

$SD(3\mathcal K)$ (within the famous K. Erdmann's classification). Our calculation relies on “a bimodule resalution” for algebras of the above family.

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

Funding agency	Grant number
Russian Foundation for Basic Research	13-01-00902

Received: 03.07.2015

English version:
Journal of Mathematical Sciences (New York), 2016, Volume 219, Issue 4, Pages 493–512
DOI: https://doi.org/10.1007/s10958-016-3122-5

Bibliographic databases:

Document Type: Article

UDC: 512.5

Language: Russian

Citation: A. I. Generalov, I. M. Zilberbord, “Hochschild cohomology for algebras of semidihedral type. V. The family

S D (3 K)

$SD(3\mathcal K)$ ”, Problems in the theory of representations of algebras and groups. Part 28, Zap. Nauchn. Sem. POMI, 435, POMI, St. Petersburg, 2015, 5–32; J. Math. Sci. (N. Y.), 219:4 (2016), 493–512

Citation in format AMSBIB

\Bibitem{GenZil15}

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

\paper Hochschild cohomology for algebras of semidihedral type.~V. The family~$SD(3\mathcal K)$

\inbook Problems in the theory of representations of algebras and groups. Part~28

\serial Zap. Nauchn. Sem. POMI

\yr 2015

\vol 435

\pages 5--32

\publ POMI

\publaddr St.~Petersburg

\mathnet{http://mi.mathnet.ru/znsl6148}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3493614}

\transl

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

\yr 2016

\vol 219

\issue 4

\pages 493--512

\crossref{https://doi.org/10.1007/s10958-016-3122-5}

Linking options:

https://www.mathnet.ru/eng/znsl6148

https://www.mathnet.ru/eng/znsl/v435/p5

Cycle of papers

Hochschild cohomology of algebras of semidihedral type. I. Group algebras of semidihedral groups
A. I. Generalov
Algebra i Analiz, 2009, 21:2, 1–51
Hochschild cohomology for algebras of semidihedral type, II. Local algebras
A. I. Generalov
Zap. Nauchn. Sem. POMI, 2011, 386, 144–202
Hochschild cohomology for algebras of semidihedral type. III. The family $SD(2\mathcal B)_2$ in characteristic 2
A. I. Generalov
Zap. Nauchn. Sem. POMI, 2012, 400, 133–157
Hochschild cohomology for algebras of semidihedral type. IV. The cohomology algebra for the family $SD(2\mathcal B)_2(k,t,c)$ in the case $c=0$
A. I. Generalov
Zap. Nauchn. Sem. POMI, 2013, 413, 45–92
Hochschild cohomology for algebras of semidihedral type. V. The family $SD(3\mathcal K)$
A. I. Generalov, I. M. Zilberbord
Zap. Nauchn. Sem. POMI, 2015, 435, 5–32
Hochschild cohomology for algebras of semidihedral type. VI. The family $SD(2\mathcal B)_2$ in characteristic different from 2
A. I. Generalov
Zap. Nauchn. Sem. POMI, 2016, 443, 61–77
Hochschild cohomology for algebras of semidihedral type. VII. Algebras with a small parameter
A. I. Generalov
Zap. Nauchn. Sem. POMI, 2016, 452, 52–69
Hochschild cohomology for algebras of semidihedral type. VIII. The family $SD(2\mathcal B)_1$
A. I. Generalov, A. A. Zaikovskiy
Zap. Nauchn. Sem. POMI, 2017, 460, 35–52
Hochschild cohomology of algebras of semidihedral type, IX: exceptional local algebras
A. I. Generalov, D. A. Nikulin
Zap. Nauchn. Sem. POMI, 2019, 478, 17–31
Hochschild cohomology of algebras of semidihedral type, X. Cohomology algebra for exceptional local algebras
A. I. Generalov
Zap. Nauchn. Sem. POMI, 2021, 500, 51–111

This publication is cited in the following 8 articles:

A. I. Generalov, I. M. Zilberbord, V. A. Rogov, “Kogomologii Khokhshilda algebr diedralnogo tipa. X. Isklyuchitelnye lokalnye algebry”, Voprosy teorii predstavlenii algebr i grupp. 39, Zap. nauchn. sem. POMI, 522, POMI, SPb., 2023, 60–83
A. I. Generalov, “Kogomologii Khokhshilda algebr poludiedralnogo tipa, X. Algebra kogomologii isklyuchitelnykh lokalnykh algebr”, Voprosy teorii predstavlenii algebr i grupp. 37, Zap. nauchn. sem. POMI, 500, POMI, SPb., 2021, 51–111
A. I. Generalov, D. A. Nikulin, “Kogomologii Khokhshilda algebr poludiedralnogo tipa, IX. Isklyuchitelnye lokalnye algebry”, Voprosy teorii predstavlenii algebr i grupp. 34, Zap. nauchn. sem. POMI, 478, POMI, SPb., 2019, 17–31
A. I. Generalov, A. V. Semenov, “Kogomologii Khokhshilda algebr kvaternionnogo tipa. IV: Algebra kogomologii dlya isklyuchitelnykh lokalnykh algebr”, Voprosy teorii predstavlenii algebr i grupp. 34, Zap. nauchn. sem. POMI, 478, POMI, SPb., 2019, 32–77
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 $2$ ”, J. Math. Sci. (N. Y.), 243:4 (2019), 535–560
A. I. Generalov, M. A. Filippov, “Hochschild cohomology for algebras of dihedral type, VII. The family $D(3\mathcal R)$ ”, J. Math. Sci. (N. Y.), 240:4 (2019), 408–427
A. I. Generalov, “Hochschild cohomology for algebras of semidihedral type. VI. The family $SD(2\mathcal B)_2$ in characteristic different from 2”, J. Math. Sci. (N. Y.), 222:4 (2017), 404–416
A. I. Generalov, “Hochschild cohomology for algebras of semidihedral type. VII. Algebras with a small parameter”, J. Math. Sci. (N. Y.), 232:5 (2018), 622–634

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

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