Fields of Toeplitz algebras for the principal symbol of regular 2-step nilpotent groups
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914207308447744 |
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| author | Cren, Clément |
| author_facet | Cren, Clément |
| contents | We show that the C*-algebra of a regular 2-step nilpotent lie group can be recovered using continuous fields of Toeplitz algebras and a crossed product. We generalize this result to polycontact manifolds in the sense of van Erp which are endowed with fields of such groups. We also investigate those manifolds with a more rigid structure, namely those modeled on H-type groups. In all those cases, there is a certain pseudodifferential calculus named filtered calculus, we show that the algebra of principal symbols can also be recovered from the field of Toeplitz algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16475 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fields of Toeplitz algebras for the principal symbol of regular 2-step nilpotent groups Cren, Clément Operator Algebras Differential Geometry Functional Analysis We show that the C*-algebra of a regular 2-step nilpotent lie group can be recovered using continuous fields of Toeplitz algebras and a crossed product. We generalize this result to polycontact manifolds in the sense of van Erp which are endowed with fields of such groups. We also investigate those manifolds with a more rigid structure, namely those modeled on H-type groups. In all those cases, there is a certain pseudodifferential calculus named filtered calculus, we show that the algebra of principal symbols can also be recovered from the field of Toeplitz algebras. |
| title | Fields of Toeplitz algebras for the principal symbol of regular 2-step nilpotent groups |
| topic | Operator Algebras Differential Geometry Functional Analysis |
| url | https://arxiv.org/abs/2512.16475 |