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Zap. Nauchn. Sem. POMI, 2014, Volume 430, Pages 74–102 (Mi znsl6085)  

This article is cited in 6 scientific papers (total in 6 papers)

Hochschild cohomology for algebras of dihedral type. V. The family $D(3\mathcal K)$ in characteristic different from 2

A. I. Generalov, I. M. Zilberbord, D. B. Romanova

St. Petersburg State University, St. Petersburg, Russia

Abstract: We compute the Hochschild cohomology groups for algebras of dihedral type which form the family $D(3\mathcal K)$ (from the famous K. Erdmann's classification) over an algebraically closed field with characteristic different from 2. In the calculation, we use the beforehand construction of the bimodule resolution for algebras from the family under discussion.

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

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English version:
Journal of Mathematical Sciences (New York), 2016, 219:3, 385–404

Bibliographic databases:

UDC: 512.5
Received: 31.10.2014

Citation: 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”, Problems in the theory of representations of algebras and groups. Part 27, Zap. Nauchn. Sem. POMI, 430, POMI, St. Petersburg, 2014, 74–102; J. Math. Sci. (N. Y.), 219:3 (2016), 385–404

Citation in format AMSBIB
\Bibitem{GenZilRom14}
\by A.~I.~Generalov, I.~M.~Zilberbord, D.~B.~Romanova
\paper Hochschild cohomology for algebras of dihedral type.~V. The family $D(3\mathcal K)$ in characteristic different from~2
\inbook Problems in the theory of representations of algebras and groups. Part~27
\serial Zap. Nauchn. Sem. POMI
\yr 2014
\vol 430
\pages 74--102
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6085}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3486764}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 219
\issue 3
\pages 385--404
\crossref{https://doi.org/10.1007/s10958-016-3115-4}


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    This publication is cited in the following articles:
    1. 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  mathnet  crossref  mathscinet  isi  elib
    2. 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
    3. 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
    4. 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  mathnet  crossref
    5. 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  mathnet  crossref
    6. 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  mathnet
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