Support Varieties for Selfinjective Algebras |
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Authors: | Karin Erdmann, Miles Holloway, Rachel Taillefer, Nicole Snashall Ø yvind Solberg |
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Affiliation: | (1) Mathematical Institute, 24–29 St. Giles, Oxford, OX1 3LB, UK;(2) Université Jean Monnet, 34 rue Francis-Baulier, 42023, St.Etienne, Cedex 2, France;(3) Department of Mathematics, University of Leicester, University Road, Leicester, LE1 7RH, UK;(4) Institutt for matematiske fag, NTNU, N–7491 Trondheim, Norway |
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Abstract: | Support varieties for any finite dimensional algebra over a field were introduced in (Proc. London Math. Soc. 88 (3) (2004) 705–732) 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 Webbs theorem is true. As a corollary of a more general result we show that Webbs theorem generalizes to finite dimensional cocommutative Hopf algebras.Received November 2003Mathematics Subject Classifications (2000) Primary: 16E40, 16G10, 16P10, 16P20; Secondary: 16G70. |
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Keywords: | Hochschild cohomology varieties finite dimensional selfinjective algebras |
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