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St. Petersburg Mathematical Journal

This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.

ISSN 1547-7371 (online) ISSN 1061-0022 (print)

The 2020 MCQ for St. Petersburg Mathematical Journal is 0.68.

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Hochschild comohology for algebras of dihedral type, VI. The family $D(2\mathcal B)(k,s,1)$
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by A. I. Generalov and D. B. Romanova
Translated by: A. I. Generalov
St. Petersburg Math. J. 27 (2016), 923-940
DOI: https://doi.org/10.1090/spmj/1427
Published electronically: September 30, 2016
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Abstract:

The Hochschild cohomology groups are calculated for algebras of dihedral type in the series $D(2\mathcal B)(k,s,c)$ (in accordance with K. Erdmann’s classification) in the case where the parameter $c\in K$ occurring in the defining relations for this series equals 1. The calculations involve the bimodule resolvent for the algebras of this type, which is also constructed in the present paper. The results are applied to refine Erdmann’s classification, specifically, it is proved that algebras corresponding to different values of $c$ represent different classes of derived equivalence, and, in particular, different classes of Morita-equivalence.
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Bibliographic Information
  • A. I. Generalov
  • Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskiĭ pr. 28, Petrodvorets, St. Petersburg 198504, Russia
  • Email: ageneralov@gmail.com
  • D. B. Romanova
  • Affiliation: School no. 642 “Earth and Universe”, Gavanskaya ul. 54, St. Petersburg 199406, Russia
  • Email: dashhh@gmail.com
  • Received by editor(s): June 10, 2015
  • Published electronically: September 30, 2016
  • Additional Notes: The first author was supported by RFBR (grant no. 13-01-00902)

    • Dedicated: Dedicated to the 70th anniversary of Sergeĭ Vladimirovich Vostokov, a remarkable mathematician and bright personality
  • © Copyright 2016 American Mathematical Society
  • Journal: St. Petersburg Math. J. 27 (2016), 923-940
  • MSC (2010): Primary 16E40
  • DOI: https://doi.org/10.1090/spmj/1427
  • MathSciNet review: 3589223