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St. Petersburg Mathematical Journal

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



Hochschild comohology for algebras of dihedral type, VI. The family $ D(2\mathcal B)(k,s,1)$

Authors: A. I. Generalov and D. B. Romanova
Translated by: A. I. Generalov
Original publication: Algebra i Analiz, tom 27 (2015), nomer 6.
Journal: St. Petersburg Math. J. 27 (2016), 923-940
MSC (2010): Primary 16E40
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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Additional Information

A. I. Generalov
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskiĭ pr. 28, Petrodvorets, St. Petersburg 198504, Russia

D. B. Romanova
Affiliation: School no. 642 “Earth and Universe”, Gavanskaya ul. 54, St. Petersburg 199406, Russia

Keywords: Hochschild cohomology groups, algebras of dihedral type, bimodule resolvent
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
Article copyright: © Copyright 2016 American Mathematical Society

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