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 $c=0$”, Problems in the theory of representations of algebras and groups. Part 24, Zap. Nauchn. Sem. POMI, 413, POMI, St. Petersburg, 2013, 45–92; J. Math. Sci. (N. Y.), 202:3 (2014), 360

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Zapiski Nauchnykh Seminarov POMI, 2013, Volume 413, Pages 45–92 (Mi znsl5659)

This article is cited in 12 scientific papers (total in 12 papers)

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

St. Petersburg State University, St. Petersburg, Russia

Full-text PDF (423 kB) Citations (12)

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Abstract: The paper continues the previous author's paper in which the bimodule resolution was constructed for algebras of semidihedral type from the family $SD(2\mathcal B)_2$. In the present paper, using this resolution we describe a multiplicative structure of the Hochschild cohomology algebra for algebras in the mentioned family over a base field of characteristic 2 under an additional assumption that the parameter $c$ containing in the defining relations of the algebras is equal to zero.

Key words and phrases: Hochschild cohomology algebra, algebras of semidihedral type, bimodule resolution.

Received: 21.03.2013

English version:
Journal of Mathematical Sciences (New York), 2014, Volume 202, Issue 3, Pages 360–394
DOI: https://doi.org/10.1007/s10958-014-2048-z

Bibliographic databases:

Document Type: Article

UDC: 512.5

Language: Russian

Citation: 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 $c=0$”, Problems in the theory of representations of algebras and groups. Part 24, Zap. Nauchn. Sem. POMI, 413, POMI, St. Petersburg, 2013, 45–92; J. Math. Sci. (N. Y.), 202:3 (2014), 360–394

Citation in format AMSBIB

\Bibitem{Gen13}

\by A.~I.~Generalov

\paper 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 $c=0$

\inbook Problems in the theory of representations of algebras and groups. Part~24

\serial Zap. Nauchn. Sem. POMI

\yr 2013

\vol 413

\pages 45--92

\publ POMI

\publaddr St.~Petersburg

\mathnet{http://mi.mathnet.ru/znsl5659}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3073058}

\transl

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

\yr 2014

\vol 202

\issue 3

\pages 360--394

\crossref{https://doi.org/10.1007/s10958-014-2048-z}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84919916536}

Linking options:

https://www.mathnet.ru/eng/znsl5659

https://www.mathnet.ru/eng/znsl/v413/p45

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 12 articles:

Citing articles in Google Scholar: Russian citations, English citations
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