A. I. Generalov, N. Yu. Kosovskaia, “Hochschild cohomology for algebras of dihedral type. IV. The family $D(2\mathcal B)(k,s,0)$”, Problems in the theory of representations of algebras and groups. Part 26, Zap. Nauchn. Sem. POMI, 423, POMI, St. Petersburg, 2014, 67–104; J. Math. Sci. (N. Y.), 209:4 (2015), 522

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Zapiski Nauchnykh Seminarov POMI, 2014, Volume 423, Pages 67–104 (Mi znsl5998)

This article is cited in 14 scientific papers (total in 14 papers)

Hochschild cohomology for algebras of dihedral type. IV. The family

$D(2\mathcal B)(k,s,0)$

A. I. Generalov^a, N. Yu. Kosovskaia^b

^a St. Petersburg State University, St. Petersburg, Russia
^b St. Petersburg State Technological University for Plant and Polymers, St. Petersburg, Russia

Full-text PDF (327 kB) Citations (14)

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Abstract: We compute the Hochschild cohomology groups for algebras of dihedral type which are contained in the family

$D(2\mathcal B)(k,s,c)$ (from the famous K. Erdmann's classification) in the case where the parameter

$c$ included in defining relations of algebras from this family is equal to zero. The calculation relies upon a construction of the bimodule resolution for algebras from the above family.

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

Received: 17.02.2014

English version:
Journal of Mathematical Sciences (New York), 2015, Volume 209, Issue 4, Pages 522–548
DOI: https://doi.org/10.1007/s10958-015-2510-6

Bibliographic databases:

Document Type: Article

UDC: 512.5

Language: Russian

Citation: A. I. Generalov, N. Yu. Kosovskaia, “Hochschild cohomology for algebras of dihedral type. IV. The family

$D(2\mathcal B)(k,s,0)$ ”, Problems in the theory of representations of algebras and groups. Part 26, Zap. Nauchn. Sem. POMI, 423, POMI, St. Petersburg, 2014, 67–104; J. Math. Sci. (N. Y.), 209:4 (2015), 522–548

Citation in format AMSBIB

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\by A.~I.~Generalov, N.~Yu.~Kosovskaia

\paper Hochschild cohomology for algebras of dihedral type.~IV. The family~$D(2\mathcal B)(k,s,0)$

\inbook Problems in the theory of representations of algebras and groups. Part~26

\serial Zap. Nauchn. Sem. POMI

\yr 2014

\vol 423

\pages 67--104

\publ POMI

\publaddr St.~Petersburg

\mathnet{http://mi.mathnet.ru/znsl5998}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3480691}

\transl

\jour J. Math. Sci. (N. Y.)

\yr 2015

\vol 209

\issue 4

\pages 522--548

\crossref{https://doi.org/10.1007/s10958-015-2510-6}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84943362773}

Linking options:

https://www.mathnet.ru/eng/znsl5998

https://www.mathnet.ru/eng/znsl/v423/p67

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

This publication is cited in the following 14 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 $D(3\mathcal K)$ 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
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, 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, 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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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