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Algebra i Analiz, 2006, Volume 18, Issue 1, Pages 55–107 (Mi aa60)  

This article is cited in 24 scientific papers (total in 24 papers)

Research Papers

Hochschild cohomology of algebras of quaternion type, I: Generalized quaternion groups

A. I. Generalov

Saint-Petersburg State University

Abstract: In terms of generators and defining relations, a description is given of the Hochschild cohomology algebra for one of the series of local algebras of quaternion type. As a corollary, the Hochschild cohomology algebra is described for the group algebras of generalized quaternion groups over algebraically closed fields of characteristic 2.

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English version:
St. Petersburg Mathematical Journal, 2007, 18:1, 37–76

Bibliographic databases:

MSC: 13D03
Received: 19.09.2005

Citation: A. I. Generalov, “Hochschild cohomology of algebras of quaternion type, I: Generalized quaternion groups”, Algebra i Analiz, 18:1 (2006), 55–107; St. Petersburg Math. J., 18:1 (2007), 37–76

Citation in format AMSBIB
\Bibitem{Gen06}
\by A.~I.~Generalov
\paper Hochschild cohomology of algebras of quaternion type, I:~Generalized quaternion groups
\jour Algebra i Analiz
\yr 2006
\vol 18
\issue 1
\pages 55--107
\mathnet{http://mi.mathnet.ru/aa60}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2225213}
\zmath{https://zbmath.org/?q=an:1139.16009}
\transl
\jour St. Petersburg Math. J.
\yr 2007
\vol 18
\issue 1
\pages 37--76
\crossref{https://doi.org/10.1090/S1061-0022-06-00942-3}


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    This publication is cited in the following articles:
    1. A. I. Generalov, “Hochschild cohomology of the integral group ring of the dihedral group. I: Even case”, St. Petersburg Math. J., 19:5 (2008), 723–763  mathnet  crossref  mathscinet  zmath  isi
    2. A. I. Generalov, A. A. Ivanov, S. O. Ivanov, “Hochschild cohomology of algebras of quaternion type. II. The family $Q(2\mathcal B)_1$ in characteristic 2”, J. Math. Sci. (N. Y.), 151:3 (2008), 2961–3009  mathnet  crossref
    3. A. I. Generalov, “Cohomology of algebras of semidihedral type. VI”, J. Math. Sci. (N. Y.), 147:5 (2007), 7074–7083  mathnet  crossref  mathscinet
    4. A. I. Generalov, “Hochschild cohomology of algebras of quaternion type. III. Algebras with a small parameter”, J. Math. Sci. (N. Y.), 156:6 (2009), 877–900  mathnet  crossref  zmath
    5. 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
    6. 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
    7. 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
    8. 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
    9. 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
    10. M. A. Pustovykh, “Hochschild cohomology ring of Möbius algebras”, J. Math. Sci. (N. Y.), 183:5 (2012), 692–714  mathnet  crossref
    11. A. I. Generalov, “Cohomology of algebras of semidihedral type. VIII”, J. Math. Sci. (N. Y.), 188:5 (2013), 582–590  mathnet  crossref  mathscinet
    12. 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
    13. 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
    14. 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
    15. 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
    16. A. A. Ivanov, “$BV$-algebra structure on Hochschild cohomology of local algebras of quaternion type in characteristic 2”, J. Math. Sci. (N. Y.), 219:3 (2016), 427–461  mathnet  crossref  mathscinet
    17. 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
    18. Ivanov A., Ivanov S.O., Volkov Yu., Zhou G., “Bv Structure on Hochschild Cohomology of the Group Ring of Quaternion Group of Order Eight in Characteristic Two”, J. Algebra, 435 (2015), 174–203  crossref  mathscinet  zmath  isi  elib  scopus
    19. 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
    20. 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
    21. 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
    22. A. I. Generalov, M. A. Filippov, “Kogomologii Khokhshilda algebr diedralnogo tipa, VII. Seriya $D(3\mathcal R)$”, Voprosy teorii predstavlenii algebr i grupp. 32, Zap. nauchn. sem. POMI, 460, POMI, SPb., 2017, 53–81  mathnet
    23. A. I. Generalov, N. Yu. Kosovskaya, “Kogomologii Khokhshilda algebr diedralnogo tipa. VIII. Algebra kogomologii dlya serii $D(2\mathcal B)(k,s,0)$ v kharakteristike $2$”, Voprosy teorii predstavlenii algebr i grupp. 33, Zap. nauchn. sem. POMI, 470, POMI, SPb., 2018, 50–87  mathnet
    24. Taillefer R., “First Hochschild Cohomology Group and Stable Equivalence Classification of Morita Type of Some Tame Symmetric Algebras”, Homol. Homotopy Appl., 21:1 (2019), 19–48  crossref  mathscinet  isi  scopus
  • Алгебра и анализ St. Petersburg Mathematical Journal
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