## Seminario

Luogo e orario: Aula 1B1, 16.00

Speaker: Jacopo Bassi

Titolo: On C*-algebras associated to the action of discrete subgroups of SL(2,R) on R^2 \{0}

Abstract: Transformation group C*-algebras set up a connection between topological dynamics and the theory of C*-algebras. In the case of discrete groups acting on compact spaces, many examples have been considered so far for which it is possible to interpret dynamical properties on the algebraic side and obtain classification results. The case of discrete groups acting on locally compact non-compact spaces still deserves a proper study and some specific examples should be investigated in order to make a first step in this direction.

In this talk I will focus on transformation group C*-algebras associated to the action of discrete subgroups of SL(2,R) on R^2 \{0} by means of matrix multiplication of vectors. I will introduce a weaker version of the "wandering on compacts" assumption that is seen to guarantee stability for a certain class of discrete subgroups of SL(2,R); in the case of cocompact subgroups further structure results are obtained by looking at the C*-algebra associated to the horocycle flow on the corresponding compact homogeneous space of SL(2,R).

Based on the Preprint: arXiv:1806.09020v1