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Zap. Nauchn. Sem. POMI, 2011, Volume 388, Pages 119–151 (Mi znsl4107)  

This article is cited in 7 scientific papers (total in 7 papers)

Hochschild cohomology for the integer group ring of the semidihedral group

A. I. Generalov

Saint-Petersburg State University, Saint-Petersburg, Russia

Abstract: We compute the Hochschild cohomology group for the integer group ring of the semidihedral 2-group $SD_{2^k}$. In calculations, we use the free bimodule resolution of the corresponding group ring. In turn, to construct that, we first construct the usual resolution of the trivial $SD_{2^k}$-module $\mathbb Z$.

Key words and phrases: Hochschild cohomology groups, semidihedral group, integer group ring.

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English version:
Journal of Mathematical Sciences (New York), 2012, 183:5, 640–657

Document Type: Article
UDC: 512.5
Received: 16.05.2011

Citation: A. I. Generalov, “Hochschild cohomology for the integer group ring of the semidihedral group”, Problems in the theory of representations of algebras and groups. Part 21, Zap. Nauchn. Sem. POMI, 388, POMI, St. Petersburg, 2011, 119–151; J. Math. Sci. (N. Y.), 183:5 (2012), 640–657

Citation in format AMSBIB
\Bibitem{Gen11}
\by A.~I.~Generalov
\paper Hochschild cohomology for the integer group ring of the semidihedral group
\inbook Problems in the theory of representations of algebras and groups. Part~21
\serial Zap. Nauchn. Sem. POMI
\yr 2011
\vol 388
\pages 119--151
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4107}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2012
\vol 183
\issue 5
\pages 640--657
\crossref{https://doi.org/10.1007/s10958-012-0829-9}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84862248086}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. I. Generalov, “Cohomology of algebras of semidihedral type. VIII”, J. Math. Sci. (N. Y.), 188:5 (2013), 582–590  mathnet  crossref  mathscinet
    2. 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  mathnet  crossref  mathscinet
    3. 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  mathnet  crossref  mathscinet
    4. A. P. Alekhin, Yu. V. Volkov, A. I. Generalov, “The Hochschild cohomology ring for modular group”, St. Petersburg Math. J., 26:1 (2015), 1–25  mathnet  crossref  mathscinet  isi  elib
    5. 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  mathnet  crossref  mathscinet
    6. 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  mathnet  crossref  mathscinet
    7. A. I. Generalov, N. Yu. Kosovskaya, “Kogomologii Khokhshilda algebr diedralnogo tipa. VIII. Algebra kogomologii dlya serii $D(2\mathcal B)(k,s,0)$ v kharakteristike $2$”, Voprosy teorii predstavlenii algebr i grupp. 33, Zap. nauchn. sem. POMI, 470, POMI, SPb., 2018, 50–87  mathnet
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