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Algebra i Analiz, 2006, Volume 18, Issue 4, Pages 39–82 (Mi aa78)  

This article is cited in 19 scientific papers (total in 19 papers)

Research Papers

Hochschild cohomology of the Liu–Schulz algebras

A. I. Generalov, N. Yu. Kosovskaya

Saint-Petersburg State University
References:
Abstract: A description of the Hochschild cohomology algebra for the symmetric 8-dimensional algebras found by Liu and Schulz is given in terms of generators and relations. The dimensions of the cohomology groups are calculated.
Received: 03.10.2005
English version:
St. Petersburg Mathematical Journal, 2007, Volume 18, Issue 4, Pages 539–572
DOI: https://doi.org/10.1090/S1061-0022-07-00960-0
Bibliographic databases:
Document Type: Article
MSC: 16E40, 16E05
Language: Russian
Citation: A. I. Generalov, N. Yu. Kosovskaya, “Hochschild cohomology of the Liu–Schulz algebras”, Algebra i Analiz, 18:4 (2006), 39–82; St. Petersburg Math. J., 18:4 (2007), 539–572
Citation in format AMSBIB
\Bibitem{GenKos06}
\by A.~I.~Generalov, N.~Yu.~Kosovskaya
\paper Hochschild cohomology of the Liu--Schulz algebras
\jour Algebra i Analiz
\yr 2006
\vol 18
\issue 4
\pages 39--82
\mathnet{http://mi.mathnet.ru/aa78}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2262583}
\zmath{https://zbmath.org/?q=an:1146.16005}
\transl
\jour St. Petersburg Math. J.
\yr 2007
\vol 18
\issue 4
\pages 539--572
\crossref{https://doi.org/10.1090/S1061-0022-07-00960-0}
Linking options:
  • https://www.mathnet.ru/eng/aa78
  • https://www.mathnet.ru/eng/aa/v18/i4/p39
  • This publication is cited in the following 19 articles:
    1. 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  mathnet
    2. 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)D(2B)(k,s,0) in characteristic 2”, J. Math. Sci. (N. Y.), 243:4 (2019), 535–560  mathnet  crossref
    3. A. I. Generalov, “Hochschild cohomology for algebras of semidihedral type. VI. The family SD(2B)2 in characteristic different from 2”, J. Math. Sci. (N. Y.), 222:4 (2017), 404–416  mathnet  crossref  mathscinet
    4. 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
    5. A. I. Generalov, I. M. Zilberbord, “Hochschild cohomology for algebras of semidihedral type. V. The family SD(3K)”, J. Math. Sci. (N. Y.), 219:4 (2016), 493–512  mathnet  crossref  mathscinet
    6. A. I. Generalov, D. B. Romanova, “Hochschild cohomology for algebras of dihedral type. VI. The family D(2B)(k,s,1)”, St. Petersburg Math. J., 27:6 (2016), 923–940  mathnet  crossref  mathscinet  isi  elib
    7. A. I. Generalov, N. Yu. Kosovskaia, “Hochschild cohomology for algebras of dihedral type. IV. The family D(2B)(k,s,0)”, J. Math. Sci. (N. Y.), 209:4 (2015), 522–548  mathnet  crossref  mathscinet
    8. A. I. Generalov, I. M. Zilberbord, D. B. Romanova, “Hochschild cohomology for algebras of dihedral type. V. The family D(3K) in characteristic different from 2”, J. Math. Sci. (N. Y.), 219:3 (2016), 385–404  mathnet  crossref  mathscinet
    9. A. I. Generalov, “Hochschild cohomology for algebras of semidihedral type. IV. The cohomology algebra for the family SD(2B)2(k,t,c) in the case c=0”, J. Math. Sci. (N. Y.), 202:3 (2014), 360–394  mathnet  crossref  mathscinet
    10. A. I. Generalov, “Hochschild cohomology for algebras of semidihedral type. III. The family SD(2B)2 in characteristic 2”, J. Math. Sci. (N. Y.), 192:2 (2013), 200–214  mathnet  crossref  mathscinet
    11. 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
    12. 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
    13. M. A. Pustovykh, “Hochschild cohomology ring of Möbius algebras”, J. Math. Sci. (N. Y.), 183:5 (2012), 692–714  mathnet  crossref
    14. A. I. Generalov, “Cohomology of algebras of semidihedral type. VIII”, J. Math. Sci. (N. Y.), 188:5 (2013), 582–590  mathnet  crossref  mathscinet
    15. 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
    16. 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
    17. 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
    18. A. I. Generalov, A. A. Ivanov, S. O. Ivanov, “Hochschild cohomology of algebras of quaternion type. II. The family Q(2B)1 in characteristic 2”, J. Math. Sci. (N. Y.), 151:3 (2008), 2961–3009  mathnet  crossref
    19. A. I. Generalov, “Cohomology of algebras of semidihedral type. VI”, J. Math. Sci. (N. Y.), 147:5 (2007), 7074–7083  mathnet  crossref  mathscinet
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