Fields of Toeplitz algebras form the principal symbol of regular 2-step nilpotent groups

Clément Cren

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arXiv · 2512.16475

Fields of Toeplitz algebras form the principal symbol of regular 2-step nilpotent groups

Clément Cren

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Abstract

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.

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Clément Cren. 2025-12-18. Fields of Toeplitz algebras form the principal symbol of regular 2-step nilpotent groups. https://arxiv.org/abs/2512.16475

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