Completions of Infinitesimal Hecke Algebras of sl2

TL;DR

This paper explores the structure of infinitesimal Hecke algebras of sl2, relating them to noncommutative deformations of Kleinian singularities, and establishes key algebraic properties and equivalences.

Contribution

It introduces a novel connection between infinitesimal Hecke algebras of sl2 and noncommutative Kleinian singularity deformations, proving new algebraic properties.

Findings

Relation between completions of infinitesimal Hecke algebras and noncommutative Kleinian singularities

Proved an analogue of Bernstein's inequality and simplicity of maximal primitive quotients

Established Skryabin type equivalence for these algebras

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.