Abstract:
We describe the Hochschild cohomology algebra for algebras of dihedral type in the subfamily of the family D(2B), for which the parameter c is equal to 0. In the calculation of multiplication in this cohomology algebra, we use the minimal bimodule projective resolution for the algebras under consideration that was constructed in the previous paper of the authors. The obtained results allow us to describe the Hochschild cohomology algebra also for algebras in the family D(2A) for which c=0.
Key words and phrases:
Hochschild cohomology algebra, algebras of dihedral type, bimodule resolution.
Citation:
A. I. Generalov, N. Yu. Kosovskaia, “Hochschild cohomology of algebras of dihedral type. VIII. The Hochschild cohomology algebra for the family D(2B)(k,s,0) in characteristic 2”, Problems in the theory of representations of algebras and groups. Part 33, Zap. Nauchn. Sem. POMI, 470, POMI, St. Petersburg, 2018, 50–87; J. Math. Sci. (N. Y.), 243:4 (2019), 535–560
\Bibitem{GenKos18}
\by A.~I.~Generalov, N.~Yu.~Kosovskaia
\paper Hochschild cohomology of algebras of dihedral type.~VIII. The Hochschild cohomology algebra for the family $D(2\mathcal B)(k,s,0)$ in characteristic~$2$
\inbook Problems in the theory of representations of algebras and groups. Part~33
\serial Zap. Nauchn. Sem. POMI
\yr 2018
\vol 470
\pages 50--87
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6611}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2019
\vol 243
\issue 4
\pages 535--560
\crossref{https://doi.org/10.1007/s10958-019-04555-9}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85074831637}
This publication is cited in the following 5 articles:
A. I. Generalov, “Kogomologii Khokhshilda algebr diedralnogo tipa. XI. Algebra kogomologii dlya nekotoroi serii isklyuchitelnykh algebr”, Voprosy teorii predstavlenii algebr i grupp. 40, Posvyaschaetsya pamyati Nikolaya Aleksandrovicha VAVILOVA, Zap. nauchn. sem. POMI, 531, POMI, SPb., 2024, 71–100
A. I. Generalov, “Kogomologii Khokhshilda algebr diedralnogo tipa. XII. Algebra kogomologii dlya serii isklyuchitelnykh algebr s dvumya prostymi modulyami”, Algebra i teoriya chisel. 7, Zap. nauchn. sem. POMI, 538, POMI, SPb., 2024, 5–44
A. I. Generalov, I. M. Zilberbord, V. A. Rogov, “Kogomologii Khokhshilda algebr diedralnogo tipa. X. Isklyuchitelnye lokalnye algebry”, Voprosy teorii predstavlenii algebr i grupp. 39, Zap. nauchn. sem. POMI, 522, POMI, SPb., 2023, 60–83
A. I. Generalov, M. A. Kachalova, P. A. Mostovskii, “Kogomologii Khokhshilda algebr diedralnogo tipa. IX. Algebra kogomologii dlya serii D(3K) v kharakteristike, otlichnoi ot 2”, Voprosy teorii predstavlenii algebr i grupp. 38, Zap. nauchn. sem. POMI, 513, POMI, SPb., 2022, 30–56
M. A. Kachalova, “Algebra kogomologii Khokhshilda isklyuchitelnykh lokalnykh algebr diedralnogo tipa”, Voprosy teorii predstavlenii algebr i grupp. 38, Zap. nauchn. sem. POMI, 513, POMI, SPb., 2022, 85–109
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