Free actions of polynomial growth Lie groups and classifiable C*-algebras

Ulrik Enstad; Gabriel Favre; Sven Raum

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arXiv · 2307.15013

Free actions of polynomial growth Lie groups and classifiable C*-algebras

Ulrik Enstad·Gabriel Favre·Sven Raum

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Abstract

We show that any free action of a connected Lie group of polynomial growth on a finite dimensional locally compact space has finite tube dimension. This is shown to imply that the associated crossed product C*-algebra has finite nuclear dimension. As an application we show that C*-algebras associated with certain aperiodic point sets in connected Lie groups of polynomial growth are classifiable. Examples include cut-and-project sets constructed from irreducible lattices in products of connected nilpotent Lie groups.

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Ulrik Enstad, Gabriel Favre, Sven Raum. 2023-07-27. Free actions of polynomial growth Lie groups and classifiable C*-algebras. https://arxiv.org/abs/2307.15013

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