Operator Algebra Seminar

Weekly Operator Algebra Seminar

Speaker: David Jondreville (REIMS)

Title: Deformation quantization for actions of a local field.

Abstract :
We shall develop the theory of deformation of C*-algebras endowed with a group action, from the perspective of non-formal equivariant quantization. This program aims to extend Rieffel's deformation theory for more general groups than R^d. In 2010, Pierre Bielavsky and Victor Gayral have constructed such a theory for a class of non-Abelian Lie groups. Here, we study the somehow opposite situation of Abelian but non-Lie groups. More specifically, we construct here a deformation theory of C*-algebras endowed with an action of a finite dimensional vector space over a non-Archimedean local field of characteristic different from 2. At the root of our construction stands the p-adic version of the Weyl quantization introduced by Haran and further extended by Bechata and Unterberger.