April 4th 2017; 12:00 auditorium CRM
Eusebio Gardella. Actions of nonamenable groups on strongly self-absorbing C*-algebras

Abstract: We study strongly outer actions of nonamenable discrete groups on unital, tracial C ∗ -algebras. For example, for a discrete group G , we show that the Bernoulli shift of G on a strongly self-absorbing C ∗ -algebra absorbs the identity on the Jiang-Su algebra tensorially if and only if the group is amenable. While it is conjectured that any two strongly outer actions of a (torsion-free) amenable group on a strongly self-absorbing C ∗ -algebra are cocycle conjugate, we show that this fails quite drastically for most nonamenable groups. A particular case of our main result implies that if G contains a copy of the free group, then there exist uncountable many, non-cocycle conjugate strongly outer actions of G on any strongly self-absorbing C*-algebra. Our methods also allow us to prove analogs of these results for actions on the hyperfinite II-1 factor, providing an alternative proof to a result of Brothier-Vaes.