## University of Sydney Algebra Seminar

# 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).