A. I. Generalov, “Hochschild cohomology of algebras of quaternion type. III. Algebras with a small parameter”, Problems in the theory of representations of algebras and groups. Part 17, Zap. Nauchn. Sem. POMI, 356, POMI, St. Petersburg, 2008, 46–84; J. Math. Sci. (N. Y.), 156:6 (2009), 877

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Zapiski Nauchnykh Seminarov POMI, 2008, Volume 356, Pages 46–84 (Mi znsl2109)

This article is cited in 19 scientific papers (total in 19 papers)

Hochschild cohomology of algebras of quaternion type. III. Algebras with a small parameter

A. I. Generalov

Saint-Petersburg State University

Full-text PDF (388 kB) Citations (19)

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Abstract: For algebras of quaternion type in the family $Q(2\mathcal B)_1$ which have a “small” natural parameter, we describe the Hochschild cohomology algebra. We use in the corresponding calculation a beforehand constructed 4-periodic bimodule resolution for the algebras under consideration. As result, we complete a description of the Hochschild cohomology algebra for all algebras of quaternion type with 2 simple modules in characteristic two. Bibl. – 7 titles.

Received: 12.06.2008

English version:
Journal of Mathematical Sciences (New York), 2009, Volume 156, Issue 6, Pages 877–900
DOI: https://doi.org/10.1007/s10958-009-9296-3

Bibliographic databases:

UDC: 512.5

Language: Russian

Citation: A. I. Generalov, “Hochschild cohomology of algebras of quaternion type. III. Algebras with a small parameter”, Problems in the theory of representations of algebras and groups. Part 17, Zap. Nauchn. Sem. POMI, 356, POMI, St. Petersburg, 2008, 46–84; J. Math. Sci. (N. Y.), 156:6 (2009), 877–900

Citation in format AMSBIB

\Bibitem{Gen08}

\by A.~I.~Generalov

\paper Hochschild cohomology of algebras of quaternion type.~III. Algebras with a~small parameter

\inbook Problems in the theory of representations of algebras and groups. Part~17

\serial Zap. Nauchn. Sem. POMI

\yr 2008

\vol 356

\pages 46--84

\publ POMI

\publaddr St.~Petersburg

\mathnet{http://mi.mathnet.ru/znsl2109}

\zmath{https://zbmath.org/?q=an:1177.16008}

\transl

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

\yr 2009

\vol 156

\issue 6

\pages 877--900

\crossref{https://doi.org/10.1007/s10958-009-9296-3}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-65049085149}

Linking options:

https://www.mathnet.ru/eng/znsl2109

https://www.mathnet.ru/eng/znsl/v356/p46

Cycle of papers

Hochschild cohomology of algebras of quaternion type, I: Generalized quaternion groups
A. I. Generalov
Algebra i Analiz, 2006, 18:1, 55–107
Hochschild cohomology of algebras of quaternion type. II. The family $Q(2\mathcal B)_1$ in characteristic 2
A. I. Generalov, A. A. Ivanov, S. O. Ivanov
Zap. Nauchn. Sem. POMI, 2007, 349, 53–134
Hochschild cohomology of algebras of quaternion type. III. Algebras with a small parameter
A. I. Generalov
Zap. Nauchn. Sem. POMI, 2008, 356, 46–84
Hochschild cohomology of algebras of quaternion type, IV: cohomology algebra for exceptional local algebras
A. I. Generalov, A. V. Semenov
Zap. Nauchn. Sem. POMI, 2019, 478, 32–77

This publication is cited in the following 19 articles:

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

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Full-text PDF :	101
References:	86

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