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 $2$”, 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

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Zapiski Nauchnykh Seminarov POMI, 2018, Volume 470, Pages 50–87 (Mi znsl6611)

This article is cited in 3 scientific papers (total in 3 papers)

Hochschild cohomology of algebras of dihedral type. VIII. The Hochschild cohomology algebra for the family $D(2\mathcal B)(k,s,0)$ in characteristic $2$

A. I. Generalov, N. Yu. Kosovskaia

St. Petersburg State University, St. Petersburg, Russia

Full-text PDF (325 kB) Citations (3)

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Abstract: We describe the Hochschild cohomology algebra for algebras of dihedral type in the subfamily of the family $D(2\mathcal B)$, 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 $D(2\mathcal A)$ for which $c=0$.

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

Funding agency	Grant number
Russian Foundation for Basic Research	17-01-00258

Received: 08.10.2018

English version:
Journal of Mathematical Sciences (New York), 2019, Volume 243, Issue 4, Pages 535–560
DOI: https://doi.org/10.1007/s10958-019-04555-9

Bibliographic databases:

Document Type: Article

UDC: 512.5

Language: Russian

Citation: 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 $2$”, 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

Citation in format AMSBIB

\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}

Linking options:

https://www.mathnet.ru/eng/znsl6611

https://www.mathnet.ru/eng/znsl/v470/p50

Cycle of papers

Hochschild cohomologies of dihedral type algebras, I: $D(3\mathcal K)$ series in characteristic 2
A. I. Generalov
Algebra i Analiz, 2004, 16:6, 53–122
Hochschild cohomology of algebras of dihedral type. II. Local algebras
A. I. Generalov
Zap. Nauchn. Sem. POMI, 2010, 375, 92–129
Hochschild cohomology for algebras of dihedral type. IV. The family $D(2\mathcal B)(k,s,0)$
A. I. Generalov, N. Yu. Kosovskaia
Zap. Nauchn. Sem. POMI, 2014, 423, 67–104
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
Zap. Nauchn. Sem. POMI, 2014, 430, 74–102
Hochschild cohomology for algebras of dihedral type. VI. The family $D(2\mathcal B)(k,s,1)$
A. I. Generalov, D. B. Romanova
Algebra i Analiz, 2015, 27:6, 89–116
Hochschild cohomology of algebras of dihedral type. VIII. The Hochschild cohomology algebra for the family $D(2\mathcal B)(k,s,0)$ in characteristic $2$
A. I. Generalov, N. Yu. Kosovskaia
Zap. Nauchn. Sem. POMI, 2018, 470, 50–87
Hochschild cohomology of algebras of dihedral type. IX. The Hochschild cohomology algebra for the family $D(3\mathcal K)$ in characteristic different from $2$
A. I. Generalov, M. A. Kachalova, P. A. Mostovskij
Zap. Nauchn. Sem. POMI, 2022, 513, 30–56
Hochschild cohomology for algebras of dihedral type. X. Exceptional local algebras
A. I. Generalov, I. M. Zilberbord, V. A. Rogov
Zap. Nauchn. Sem. POMI, 2023, 522, 60–83
Hochschild cohomology of algebras of dihedral type. XI. Cohomology algebra for a family of exceptional algebras
A. I. Generalov
Zap. Nauchn. Sem. POMI, 2024, 531, 71–100
Hochschild cohomology of algebras of dihedral type. XII. Cohomology algebra for a family of exceptional algebras with two simple modules
A. I. Generalov
Zap. Nauchn. Sem. POMI, 2024, 538, 5–44

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