authors:
1) Karin Erdmann
Mathematical Institute, 24-29 St Giles, Oxford, OX1 3LB, UK

2) Miles Holloway
Mathematical Institute, 24-29 St Giles, Oxford, OX1 3LB, UK

3) Nicole Snashall
Department of Mathematics, University of Leicester LE1 7RH, UK

4) Oyvind Solberg
Institutt for Matematiske FAG, NTNU, N-7491 Trondheim, Norway

5)Rachel Taillefer
Département de Mathématiques, Faculté des Sciences et
Techniques, 23 rue du Docteur Paul Michelon, 42023 Saint-Etienne cedex 2,
France.

abstract:
Support varieties for any finite dimensional algebra over a 
field were introduced by Snashall-Solberg using graded subalgebras 
of the Hochschild cohomology ring. We mainly study these varieties 
for selfinjective algebras under appropriate finite generation hypotheses. 
Then many of the standard results from the theory of support varieties 
for finite groups generalize to this situation. In particular, 
the complexity of the module equals the dimension of its 
corresponding variety, all closed homogeneous varieties occur as the 
variety of some module, the variety of an indecomposable module 
is connected, the variety of periodic modules are 
lines and for symmetric algebras 
a generalization of Webb's theorem is true.
As a corollary of a more general result we show that Webb's 
theorem generalizes to finite dimensional 
cocommutative Hopf algebras.

Status:
Accepted for publication in K theory.
See
www.kluweronline.com/issn/0920-3036