**Venue**: Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Sala Seminari "-1"**At**: 14:00

**Speaker**:

- Ivan Penkov (Jacobs University Bremen)

**Abstract**:

In this talk I will describe some interesting categories of representations of infinite matrix Lie algebras. These categories are tensor categories and can be thought of as "direct limits of categories of tensor representations over finite-dimensional Lie algebras". In contrast with the finite-dimensional case, the new categories are not semisimple and not rigid. However, they are universal in a natural sense. A key to understanding the structure of the categories is that they are ordered categories, a notion which I will introduce. An interplay of restricted duals and full algebraic duals of representations makes these categories look like analogues of some objects in classical functional analysis.

**Contact person**: Willem Adriaan De Graaf