Completions of Infinitesimal Hecke Algebras of sl2

Abstract

We relate completions of infinitesimal Hecke algebras of sl2 to noncommutative deformations of Kleinian singularities of type D of Crawley-Boevey and Holland. As a consequence, we show an analogue of the inequality of Bernstein and simplicity of generic maximal primitive quotients of these algebras. We also establish Skryabin type equivalence for these algebras.

11 pages, significantly different from the previous version. The proof of Bernstein's inequality for symplectic reflection algebras was incorrect and has been removed. Current version only deals with infinitesimal Hecke algebras of sl2

References in corpus (2)

• Category O over a deformation of the symplectic oscillator algebra
• Deformations of type D Kleinian singularities