SUPPORT VARIETIES FOR SELFINJECTIVE ALGEBRAS

By Karin Erdmann Miles Holloway Nicole Snashall Oyvind Solb Taillefer. 2003

130 citations recorded by the source corpus.

Support varieties for any finite dimensional algebra over a field were introduced in (20) using graded subalgebras of the Hochschild cohomol- ogy. We mainly study these varieties for selfinjective algebras under appropri- ate finite generation hypotheses. Then many of the standard results from the theory of support varieties for finite groups generalize to this situation. In par- ticular, 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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f83cade47f6d9bce03c5bd5e7e19f83167951a79

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In Algebra and Number Theory

1. S. Iyengar
2. N. Snashall
3. S. Witherspoon
4. L. Avramov
5. J. Pevtsova
6. Eric Friedlander
7. R. Buchweitz
8. Oyvind Solberg

In Geometry and Topology

1. S. Iyengar
2. S. Witherspoon
3. L. Avramov
4. N. Snashall
5. J. Pevtsova
6. Eric Friedlander
7. R. Buchweitz
8. Jon F. Carlson

In Mathematical Physics

1. J. Pevtsova
2. S. Witherspoon
3. L. Avramov
4. Eric Friedlander
5. N. Snashall
6. S. Iyengar
7. Jon F. Carlson
8. R. Buchweitz

Citations in the corpus

• MULTIPLICATIVE STRUCTURES FOR KOSZUL ALGEBRAS (2005, background): “More generally, this connection between representation theory of finite dimensional algebras and Artin-Schelter regular Koszul algebras allows one to apply the theory of support varieties for finite dimensional selfinjective algebras defined via the Hochschild cohomology ring (see [ 4 , 16]).”
• Varieties for Modules of Quantum Elementary Abelian Groups (2006, methodology): “We must verify that Λ and H satisfy the properties required by the theory of support varieties defined via Hochschild cohomology in [16]: As Λ is local, it is an indecomposable algebra.”
• Modules of constant Jordan type (2007, result): “Namely, a result of [15] (see also [17]) following earlier work of Webb [29] asserts that if kG has wild representation type then the AuslanderReiten component of the trivial module has a very restricted form.”
• The hochschild cohomology ring of a class of special biserial algebras (2008, unknown): “We then determine explicitly the Hochschild cohomology ring modulo nilpotence, HH∗(ΛN )/N , where N is the ideal of HH ∗(ΛN) generated by all homogeneous nilpotent elements.”
• Gorenstein categories, singular equivalences and finite generation of cohomology rings in recollements (2014, unknown): “Applications and Examples 31 References 40”
• Constructing modules with prescribed cohomological support (2007, background): “Parallel theories have been constructed for finitely generated modules over finite dimensional self-injective algebras, [12, 22], and over local complete intersection rings, [1, 2].”