# Sharygin G. Quasi-differential operators on universal enveloping algebras and their applications (abstract)

In my talk I will describe a family of operators on the universal enveloping algebras, first of all on $\displaystyle{ Ugl_n }$, which were first introduced by Gourevich and Saponov. We will discuss their properties, alternative definitions and relation with the algebra of differential operators on the corresponding Lie group. We shall also speculate on the possible applications of these operators to Vinberg's question to describe argument shift subalgebras in the universal enveloping algebras.