# Slava Futorny (University of Sao Paulo)

## Friday 23 September, 12:05-12:55pm, Carslaw 175

### Torsion theories and corresponding representations

We will discuss torsion theories for representations of an important class of associative algebras which includes all finite $$W$$-algebras of type $$A$$, in particular the universal enveloping algebra of $$\mathfrak{gl}(n)$$ for all $$n$$. If $$U$$ is such an algebra which contains a finitely generated commutative subalgebra $$G$$, then the coheight of the associated prime ideals of $$G$$ is an invariant of a given simple $$U$$-module. This implies a stratification of the category of $$U$$-modules controlled by the coheight of associated prime ideals of $$G$$. This approach allows in particular to study representations of $$\mathfrak{gl}(n)$$ beyond the classical category of weight or generalized weight modules. The talk is based on recent joint results with S.Ovsienko (Kiev) and M.Saorin (Murcia).