A. I. Generalov, “Hochschild cohomology of algebras of semidihedral type. I. Group algebras of semidihedral groups”, Algebra i Analiz, 21:2 (2009), 1–51; St. Petersburg Math. J., 21:2 (2010), 163

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Algebra i Analiz, 2009, Volume 21, Issue 2, Pages 1–51 (Mi aa1003)

This article is cited in 22 scientific papers (total in 22 papers)

Hochschild cohomology of algebras of semidihedral type. I. Group algebras of semidihedral groups

A. I. Generalov

St. Petersburg State University, Department of Mathematics and Mechanics, St. Petersburg, Russia

Full-text PDF (472 kB) Citations (22)

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Abstract: For a family of local algebras of semidihedral type over an algebraically closed field of characteristic 2, the Hochschild cohomology algebra is described in terms of generators and relations. The calculations are based on the construction of a bimodule resolution for the algebras in question. As a consequence, the Hochschild cohomology algebra is described for the group algebras of semidihedral groups.

Keywords: algebras of semidihedral type, Hochschild cohomology, semidihedral groups.

Received: 01.09.2008

English version:
St. Petersburg Mathematical Journal, 2010, Volume 21, Issue 2, Pages 163–201
DOI: https://doi.org/10.1090/S1061-0022-10-01089-7

Bibliographic databases:

MSC: 13D03

Language: Russian

Citation: A. I. Generalov, “Hochschild cohomology of algebras of semidihedral type. I. Group algebras of semidihedral groups”, Algebra i Analiz, 21:2 (2009), 1–51; St. Petersburg Math. J., 21:2 (2010), 163–201

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/aa1003

https://www.mathnet.ru/eng/aa/v21/i2/p1

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 22 articles:

A. I. Generalov, “Hochschild Cohomology for Algebras of Semidihedral Type. X. Cohomology Algebra for the Exceptional Local Algebras”, J Math Sci, 272:3 (2023), 376
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
Taillefer R., “First Hochschild Cohomology Group and Stable Equivalence Classification of Morita Type of Some Tame Symmetric Algebras”, Homol. Homotopy Appl., 21:1 (2019), 19–48
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
A. I. Generalov, I. M. Zilberbord, “Hochschild cohomology for algebras of semidihedral type. V. The family $SD(3\mathcal K)$ ”, J. Math. Sci. (N. Y.), 219:4 (2016), 493–512
A. I. Generalov, D. B. Romanova, “Hochschild cohomology for algebras of dihedral type. VI. The family $D(2\mathcal B)(k,s,1)$ ”, St. Petersburg Math. J., 27:6 (2016), 923–940
A. I. Generalov, N. Yu. Kosovskaia, “Hochschild cohomology for algebras of dihedral type. IV. The family $D(2\mathcal B)(k,s,0)$ ”, J. Math. Sci. (N. Y.), 209:4 (2015), 522–548
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”, J. Math. Sci. (N. Y.), 219:3 (2016), 385–404
A. I. Generalov, “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 $c=0$ ”, J. Math. Sci. (N. Y.), 202:3 (2014), 360–394
A. I. Generalov, “Hochschild cohomology for algebras of semidihedral type. III. The family $SD(2\mathcal B)_2$ in characteristic 2”, J. Math. Sci. (N. Y.), 192:2 (2013), 200–214
A. I. Generalov, “Hochschild cohomology for algebras of semidihedral type, II. Local algebras”, J. Math. Sci. (N. Y.), 180:3 (2012), 278–314
M. A. Pustovykh, “Hochschild cohomology ring of Möbius algebras”, J. Math. Sci. (N. Y.), 183:5 (2012), 692–714
A. I. Generalov, “Cohomology of algebras of semidihedral type. VIII”, J. Math. Sci. (N. Y.), 188:5 (2013), 582–590
A. I. Generalov, “Hochschild cohomology of algebras of dihedral type. II. Local algebras”, J. Math. Sci. (N. Y.), 171:3 (2010), 357–379
Generalov A.I., “Kogomologii Khokhshilda algebr diedralnogo tipa. III. Lokalnye algebry v kharakteristike 2”, Vestn. Sankt-Peterburgskogo un-ta. Ser. 1: Matem., Mekh., Astron., 2010, no. 1, 28–38

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

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