The Hochschild cohomology ring of a selfinjective algebra of finite representation type

Authors:
Edward L. Green, Nicole Snashall and Øyvind Solberg

Journal:
Proc. Amer. Math. Soc. **131** (2003), 3387-3393

MSC (2000):
Primary 16E40, 16G10, 16G60

DOI:
https://doi.org/10.1090/S0002-9939-03-06912-0

Published electronically:
February 24, 2003

MathSciNet review:
1990627

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Abstract: This paper describes the Hochschild cohomology ring of a selfinjective algebra of finite representation type over an algebraically closed field , showing that the quotient of the Hochschild cohomology ring by the ideal generated by all homogeneous nilpotent elements is isomorphic to either or , and is thus finitely generated as an algebra. We also consider more generally the property of a finite dimensional algebra being selfinjective, and as a consequence show that if all simple -modules are -periodic, then is selfinjective.

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Additional Information

**Edward L. Green**

Affiliation:
Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061–0123

Email:
green@math.vt.edu

**Nicole Snashall**

Affiliation:
Department of Mathematics and Computer Science, University of Leicester, University Road, Leicester, LE1 7RH, England

Email:
N.Snashall@mcs.le.ac.uk

**Øyvind Solberg**

Affiliation:
Institutt for matematiske fag, NTNU, N–7491 Trondheim, Norway

Email:
oyvinso@math.ntnu.no

DOI:
https://doi.org/10.1090/S0002-9939-03-06912-0

Received by editor(s):
December 5, 2001

Received by editor(s) in revised form:
June 17, 2002

Published electronically:
February 24, 2003

Communicated by:
Martin Lorenz

Article copyright:
© Copyright 2003
American Mathematical Society