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(2B)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.
Citation:
A. I. Generalov, “Hochschild cohomology for algebras of semidihedral type. IV. The cohomology algebra for the family SD(2B)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
\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}
This publication is cited in the following 12 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
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
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