Support varieties and the Hochschild cohomology ring modulo nilpotence

Abstract

This is a survey paper based on my talks at the 41st Symposium on Ring Theory and Representation Theory, held in Shizuoka University, Japan in September 2008, and will appear in the conference proceedings. The paper begins with a brief introduction to the use of Hochschild cohomology in developing the theory of support varieties for a module over an artin algebra, by Snashall and Solberg (Proc. London Math. Soc.(3) 88 (2004), 705-732). The paper then describes the current status of research concerning the structure of the Hochschild cohomology ring modulo nilpotence.

Very minor corrections/changes

References in corpus (5)

• Support varieties for selfinjective algebras
• Multiplicative structures for Koszul algebras
• Resolutions over Koszul algebras
• Periodic resolutions and self-injective algebras of finite type
• Representation theory of liftings of quantum planes

Cited by in corpus (9)

• Monoidal categories and the Gerstenhaber bracket in Hochschild cohomology
• More counterexamples to Happel's question and Snashall-Solberg's conjecture
• Homological epimorphisms, recollements and Hochschild cohomology - with a conjecture by Snashall-Solberg in view
• Rigidity dimension - a homological dimension measuring resolutions of algebras by algebras of finite global dimension
• Bracket structure on Hochschild cohomology of Koszul quiver algebras using homotopy liftings
• Cup product on Hochschild cohomology of a family of quiver algebras
• Hochschild cohomology for a class of some self-injective special biserial algebras of rank four
• Centers of partly (anti-)commutative quiver algebras and finite generation of the Hochschild cohomology ring
• On Hochschild cohomology of a self-injective special biserial algebra obtained by a circular quiver with double arrows