Speaker
Dr
Clement Cren
(University Gustav Eiffel)
Description
In their 2014 article, Debord and Skandalis related the extension of the order 0 pseudodifferential operators algebra and the one of Connes tangent groupoid C-algebra. We show a similar result for the calculus on filtered manifolds. The theorem relies on a structure result for the symbol algebra. This result is the analog of Epstein and Melrose decomposition of symbols on contact manifolds. This structure is tied to the representation theory of nilpotent Lie groups. Similar results were obtained in 2020 by Ewert, we give a version of them using basic properties of crossed products and bundles of C*-algebras. Our structure result is based on Pedersen's fine stratification of the dual Lie algebra of a nilpotent Lie group.
