Journal of Mathematical Sciences

, Volume 171, Issue 3, pp 338–343 | Cite as

On the construction of bimodule resolutions with the help of the Happel lemma

Article

A criterion for the sequence obtained with the help of Happel’s lemma to be a minimal bimodule projective resolution is proved. This criterion is used to construct a bimodule resolution for a family of self-injective algebras of tree class D4. Bibliography: 6 titles.

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References

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    D. Happel, “Hochschild cohomology of finite-dimensional algebras,” Lect. Notes Math., 1404, 108–126 (1989).CrossRefMathSciNetGoogle Scholar
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    A. I. Generalov and M. A. Kachalova, “A bimodule resolution of a Möbius algebra,” Zap. Nauchn. Semin. POMI, 321, 36–66 (2005).MATHGoogle Scholar
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    Yu. V. Volkov and A. I. Generalov, “The Hochschild cohomology of self-injective algebras of tree type D n. I,” Zap. Nauchn. Semin. POMI, 343, 121–182 (2007).MathSciNetGoogle Scholar
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    Yu. V. Volkov, “The Hochschild cohomology of self-injective algebras of tree type D n. II,” Zap. Nauchn. Semin. POMI, 365, 63–121 (2009).Google Scholar
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    A. I. Generalov, A. A. Ivanov, and S. O. Ivanov, “The Hochschild cohomology of algebras of quaternion type. II: the series Q(2B)1 in characteristic 2,” Zap. Nauchn. Semin. POMI, 349, 53–134 (2007).Google Scholar
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    Yu. V. Volkov, “The lasses of stable equivalence of self-injective algebras of tree type D n,” Vestn. SPGU, Ser. I, Mat. Mech. Astr, No. 1, 15–21 (2008).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  • Yu. V. Volkov
    • 1
  • A. I. Generalov
    • 1
  • S. O. Ivanov
    • 1
  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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