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

JOURNAL OF ALGEBRA

卷:351

Article

Shepler, Anne V.¹  Witherspoon, Sarah² 

[1] Univ N Texas, Dept Math, Denton, TX 76203 USA

[2] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

关键词: Hochschild cohomology;    Gerstenhaber bracket;    Symplectic reflection algebras;    Deformations;    Graded Hecke algebras;    Skew group algebras;   

DOI  :  10.1016/j.jalgebra.2011.10.038

来源: Elsevier

【 摘 要 】

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. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free