| Résume | For a countable discrete group G, the group von Neumann algebra L(G) is a factor if and only if G is an `icc' group. For general locally compact groups, such an intrinsic characterization is a challenging open problem. A large class of examples in the literature of factors coming from non-discrete groups are from semidirect products, where one often gets the freedom of exploiting ergodic theoretic techniques. We will state some recent factoriality results for a class of semidirect product groups N \rtimes G where N is an abelian group of Lie type. Factoriality of such groups is integrally connected to the question of ergodicity of linear actions on R^n. This talk is based on joint work with Chinmay Tamhankar. |
