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Zap. Nauchn. Sem. POMI, 2008, Volume 356, Pages 46–84 (Mi znsl2109)  

This article is cited in 18 scientific papers (total in 18 papers)

Hochschild cohomology of algebras of quaternion type. III. Algebras with a small parameter

A. I. Generalov

Saint-Petersburg State University

Abstract: For algebras of quaternion type in the family $Q(2\mathcal B)_1$ which have a “small” natural parameter, we describe the Hochschild cohomology algebra. We use in the corresponding calculation a beforehand constructed 4-periodic bimodule resolution for the algebras under consideration. As result, we complete a description of the Hochschild cohomology algebra for all algebras of quaternion type with 2 simple modules in characteristic two. Bibl. – 7 titles.

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English version:
Journal of Mathematical Sciences (New York), 2009, 156:6, 877–900

Bibliographic databases:

UDC: 512.5
Received: 12.06.2008

Citation: A. I. Generalov, “Hochschild cohomology of algebras of quaternion type. III. Algebras with a small parameter”, Problems in the theory of representations of algebras and groups. Part 17, Zap. Nauchn. Sem. POMI, 356, POMI, St. Petersburg, 2008, 46–84; J. Math. Sci. (N. Y.), 156:6 (2009), 877–900

Citation in format AMSBIB
\Bibitem{Gen08}
\by A.~I.~Generalov
\paper Hochschild cohomology of algebras of quaternion type.~III. Algebras with a~small parameter
\inbook Problems in the theory of representations of algebras and groups. Part~17
\serial Zap. Nauchn. Sem. POMI
\yr 2008
\vol 356
\pages 46--84
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl2109}
\zmath{https://zbmath.org/?q=an:1177.16008}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2009
\vol 156
\issue 6
\pages 877--900
\crossref{https://doi.org/10.1007/s10958-009-9296-3}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-65049085149}


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    This publication is cited in the following articles:
    1. A. I. Generalov, “Hochschild cohomology of algebras of semidihedral type. I. Group algebras of semidihedral groups”, St. Petersburg Math. J., 21:2 (2010), 163–201  mathnet  crossref  mathscinet  zmath  isi
    2. A. I. Generalov, “Cohomology of algebras of semidihedral type. VII. Local algebras”, J. Math. Sci. (N. Y.), 161:4 (2009), 530–536  mathnet  crossref  zmath
    3. A. I. Generalov, “Hochschild cohomology of algebras of dihedral type. II. Local algebras”, J. Math. Sci. (N. Y.), 171:3 (2010), 357–379  mathnet  crossref
    4. A. I. Generalov, “Hochschild cohomology for algebras of semidihedral type, II. Local algebras”, J. Math. Sci. (N. Y.), 180:3 (2012), 278–314  mathnet  crossref
    5. A. I. Generalov, “Hochschild cohomology for the integer group ring of the semidihedral group”, J. Math. Sci. (N. Y.), 183:5 (2012), 640–657  mathnet  crossref
    6. A. A. Ivanov, “Hochschild cohomology of algebras of quaternion type. The family $Q(2\mathcal B)_1$ in characteristic 3”, J. Math. Sci. (N. Y.), 183:5 (2012), 658–674  mathnet  crossref
    7. M. A. Pustovykh, “Hochschild cohomology ring of Möbius algebras”, J. Math. Sci. (N. Y.), 183:5 (2012), 692–714  mathnet  crossref
    8. A. I. Generalov, “Cohomology of algebras of semidihedral type. VIII”, J. Math. Sci. (N. Y.), 188:5 (2013), 582–590  mathnet  crossref  mathscinet
    9. A. I. Generalov, “Hochschild cohomology for algebras of semidihedral type. III. The family $SD(2\mathcal B)_2$ in characteristic 2”, J. Math. Sci. (N. Y.), 192:2 (2013), 200–214  mathnet  crossref  mathscinet
    10. A. I. Generalov, “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 $c=0$”, J. Math. Sci. (N. Y.), 202:3 (2014), 360–394  mathnet  crossref  mathscinet
    11. 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  mathnet  crossref  mathscinet
    12. 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  mathnet  crossref  mathscinet
    13. 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  mathnet  crossref  mathscinet
    14. 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
    15. 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
    16. 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
    17. 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
    18. 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
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