Infinitesimal Hecke algebra of sl_2 in positive characteristic

TL;DR

This paper studies an infinitesimal Hecke algebra of sl_2 over fields with positive characteristic, revealing its structure as a finitely generated module over its center and the coincidence of its smooth and Azumaya loci.

Contribution

It establishes the finite generation over the center and the equivalence of smooth and Azumaya loci for this algebra in positive characteristic.

Findings

The algebra is finitely generated over its center.

The smooth and Azumaya loci of the center coincide.

Abstract

In this paper we consider an infinitesimal Hecke algebra of $sl_2$ in positive characteristic. We show that it is a finitely generated module over its center, and the smooth and the Azumaya loci of its center coincide.