Filtered Calculus and crossed products by R-actions

Clément Cren

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arXiv · 2308.13532

Filtered Calculus and crossed products by R-actions

Clément Cren

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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.

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Clément Cren. 2023-08-10. Filtered Calculus and crossed products by R-actions. https://arxiv.org/abs/2308.13532

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