Manuel Saorin
Universidad de Murcia, Spain
Lifting of torsion theories from commutative subalgebras.
Abstract: Inspired by some patterns on enveloping algebras of Lie algebras and (deformation of) groups rings, we study the following problem. Being given an (always associative unital) algebra U and a suitable commutative Noetherian Harish-Chandra subalgebra \Gamma, when does a hereditary torsion theory in the category of \Gamma-modules lifts to one in the category of U-modules?. The problem is pertinent since torsion theories over commutative Noetherian algebras are very well understood. From the main result of the talk we will derive a stratification of simple U-modules determined by the coheights of the prime ideals of \Gamma, which has potential applications in the study of irreducible representations of Lie algebras.