FREE ACTIONS OF POLYNOMIAL GROWTH LIE GROUPS AND CLASSIFIABLE C*-ALGEBRAS
Abstract
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.
Fields of Study & Subjects
Advanced Operator Algebra Research
Advanced Topics in Algebra
Algebraic structures and combinatorial models
Publication details
- Journal / source
- Journal of the Institute of Mathematics of Jussieu
- Publisher
- Cambridge University Press (CUP)
- Volume
- 25
- Issue
- 6
- Pages
- 1–38
- Publication date
- 23 September 2026
- Language
- EN