Filtered Calculus and crossed products by R-actions

2023/08/10 by Cren, Clément
#Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2308.13532

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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