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Zap. Nauchn. Sem. POMI, 2007, Volume 349, Pages 53–134 (Mi znsl54)  

This article is cited in 20 scientific papers (total in 20 papers)

Hochschild cohomology of algebras of quaternion type. II. The family $Q(2\mathcal B)_1$ in characteristic 2

A. I. Generalov, A. A. Ivanov, S. O. Ivanov

Saint-Petersburg State University

Abstract: In the present paper, the Hochschild cohomology is investigated for algebras of quaternion type from the family $Q(2\mathcal B)_1$ over an algebraically closed field with characteristic 2. The 4-periodic bimodule resolution is constructed for the most part of algebras of this family. Using this resolution, the description in terms of generators and relations is given for the Hochschild cohomology algebra of the algebras under consideration.

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English version:
Journal of Mathematical Sciences (New York), 2008, 151:3, 2961–3009

UDC: 512.5
Received: 12.10.2007

Citation: 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”, Problems in the theory of representations of algebras and groups. Part 16, Zap. Nauchn. Sem. POMI, 349, POMI, St. Petersburg, 2007, 53–134; J. Math. Sci. (N. Y.), 151:3 (2008), 2961–3009

Citation in format AMSBIB
\Bibitem{GenIvaIva07}
\by A.~I.~Generalov, A.~A.~Ivanov, S.~O.~Ivanov
\paper Hochschild cohomology of algebras of quaternion type.~II. The family $Q(2\mathcal B)_1$ in characteristic~2
\inbook Problems in the theory of representations of algebras and groups. Part~16
\serial Zap. Nauchn. Sem. POMI
\yr 2007
\vol 349
\pages 53--134
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl54}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2008
\vol 151
\issue 3
\pages 2961--3009
\crossref{https://doi.org/10.1007/s10958-008-9017-3}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-49249136069}


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    This publication is cited in the following articles:
    1. 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
    2. 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
    3. 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
    4. Y. V. Volkov, A. I. Generalov, S. O. Ivanov, “On construction of bimodule resolutions with the help of Happel's lemma”, J. Math. Sci. (N. Y.), 171:3 (2010), 338–343  mathnet  crossref
    5. 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
    6. 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
    7. 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
    8. 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
    9. M. A. Pustovykh, “Hochschild cohomology ring of Möbius algebras”, J. Math. Sci. (N. Y.), 183:5 (2012), 692–714  mathnet  crossref
    10. A. I. Generalov, “Cohomology of algebras of semidihedral type. VIII”, J. Math. Sci. (N. Y.), 188:5 (2013), 582–590  mathnet  crossref  mathscinet
    11. 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
    12. 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
    13. 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
    14. 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
    15. 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
    16. 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
    17. 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
    18. 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
    19. 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
    20. 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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