Filtered Calculus and crossed products by R-actions
Abstract
We show an isomorphism between the kernel of the C*-algebra of the tangent groupoid of a filtered manifold and the crossed product of the order 0 pseudodifferential operators in the associated filtered calculus by a natural R-action. This isomorphism is constructed in the same way as in the classical pseudodifferential calculus by Debord and Skandalis. The proof however relies on a structure result for the C*-algebra of graded nilpotent Lie groups which did not appear in the commutative case. A consequence of this structure result is a decomposition of the principal symbol algebra, generalizing the decomposition of Epstein and Melrose in the case of contact manifolds.
Keywords
Cite
@article{arxiv.2308.13532,
title = {Filtered Calculus and crossed products by R-actions},
author = {Clément Cren},
journal= {arXiv preprint arXiv:2308.13532},
year = {2025}
}
Comments
Structure of the paper rearranged. New section extending the spectrum decompositions to families of groups. Some changes in the notations and proofs to improve readability