Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

Hochschild cohomology of algebras of dihedral type, I: The family $ D(3\mathcal K)$ in characteristic $ 2$


Author: A. I. Generalov
Translated by: the author
Original publication: Algebra i Analiz, tom 16 (2004), nomer 6.
Journal: St. Petersburg Math. J. 16 (2005), 961-1012
MSC (2000): Primary 16E40
Published electronically: November 22, 2005
MathSciNet review: 2117449
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In terms of generators and defining relations, the Hochschild cohomology algebras are described for all algebras of dihedral type in the family $ D(3\mathcal{K})$ over an algebraically closed field of characteristic $ 2$. The results are applied to three other families of algebras of dihedral type, namely, $ D(3\mathcal{A})_1$, $ D(3\mathcal{B})_1$, and $ D(3\mathcal{D})_1$. As a corollary, a description is obtained for the Hochschild cohomology algebra for blocks with dihedral defect group and three simple modules; in particular, this applies to principal blocks of the groups $ \operatorname{PSL}(2,q)$ with odd $ q$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2000): 16E40

Retrieve articles in all journals with MSC (2000): 16E40


Additional Information

A. I. Generalov
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskiĭ Prospekt 28, Staryĭ Peterhof, St. Petersburg 198904, Russia

DOI: http://dx.doi.org/10.1090/S1061-0022-05-00886-1
PII: S 1061-0022(05)00886-1
Keywords: Algebras of dihedral type, Hochschild cohomology
Received by editor(s): March 17, 2004
Published electronically: November 22, 2005
Article copyright: © Copyright 2005 American Mathematical Society