Group actions on algebras and the graded Lie structure of Hochschild cohomology

Details Group actions on algebras and the graded Lie structure of Hochschild cohomology Group actions on algebras and the graded Lie structure of Hochschild cohomology

2009-11-04

arxiv.org/abs/0911.0938v2

Mathematics

Rings and Algebras

Title changed; 39 pages

Scientific paper

Hochschild cohomology governs deformations of algebras, and its graded Lie structure plays a vital role. We study this structure for the Hochschild cohomology of the skew group algebra formed by a finite group acting on an algebra by automorphisms. We examine the Gerstenhaber bracket with a view toward deformations and developing bracket formulas. We then focus on the linear group actions and polynomial algebras that arise in orbifold theory and representation theory; deformations in this context include graded Hecke algebras and symplectic reflection algebras. We give some general results describing when brackets are zero for polynomial skew group algebras, which allow us in particular to find noncommutative Poisson structures. For abelian groups, we express the bracket using inner products of group characters. Lastly, we interpret results for graded Hecke algebras.

Affiliated with

Also associated with

No associations

Rating

Group actions on algebras and the graded Lie structure of Hochschild cohomology does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Group actions on algebras and the graded Lie structure of Hochschild cohomology, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Group actions on algebras and the graded Lie structure of Hochschild cohomology will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-417535