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Support varieties for selfinjective algebras

Karin Erdmann·Miles Holloway·Nicole Snashall·Oyvind Solberg·Rachel Taillefer
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Abstract

Support varieties for any finite dimensional algebra over a field were introduced by Snashall-Solberg using graded subalgebras of the Hochschild cohomology. 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, periodic modules are lines and for symmetric algebras a generalization of Webb's theorem is true.

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Karin Erdmann, Miles Holloway, Nicole Snashall, Oyvind Solberg, Rachel Taillefer. 2003-11-18. Support varieties for selfinjective algebras. https://doi.org/10.1007/s10977-004-0838-7

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