Operator Algebra Seminar

Speaker:  Olivier Gabriel (Copenhagen)

Title: Ergodic actions and Hodge theory for C*-algebras

Abstract : We start by an introduction regarding the notion of spectral triples and the motivations behind it. We then discuss a class of spectral triples obtained from ergodic actions of compact Lie groups on C*-algebras. For this class, we show that a Hodge theory is available, namely: we have differential forms, Hodge-de Rham operators and a Hodge decomposition theorem. It follows that we can easily introduce conformal deformations for this class. Finally, we investigate the analytical properties of the Hodge-de Rham operator and prove that it is selfadjoint and finitely summable.