Filtered Calculus and crossed products by R-actions
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908303022358528 |
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| author | Cren, Clément |
| author_facet | Cren, Clément |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_13532 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Filtered Calculus and crossed products by R-actions Cren, Clément Operator Algebras Differential Geometry Functional Analysis 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. |
| title | Filtered Calculus and crossed products by R-actions |
| topic | Operator Algebras Differential Geometry Functional Analysis |
| url | https://arxiv.org/abs/2308.13532 |