Polynomial growth and property $RD_p$ for \'etale groupoids with applications to $K$-theory

Are Austad; Eduard Ortega; Mathias Palmstrøm

Polynomial growth and property $RD_p$ for \'etale groupoids with applications to $K$-theory

Operator Algebras 2024-02-27 v3 Functional Analysis K-Theory and Homology

Authors: Are Austad , Eduard Ortega , Mathias Palmstrøm

Abstract

We investigate property $RD_p$ for \'etale groupoids and apply it to $K$ -theory of reduced groupoid $L^p$ -operator algebras. In particular, under the assumption of polynomial growth, we show that the $K$ -theory groups for a reduced groupoid $L^p$ -operator algebra are independent of $p\in (1, \infty)$ . We apply the results to coarse groupoids and graph groupoids.

Keywords

etale groupoids property RD_p polynomial growth K-theory reduced groupoid L^p-operator algebras coarse groupoids graph groupoids

Cite

@article{arxiv.2304.14458,
  title  = {Polynomial growth and property $RD_p$ for \'etale groupoids with applications to $K$-theory},
  author = {Are Austad and Eduard Ortega and Mathias Palmstrøm},
  journal= {arXiv preprint arXiv:2304.14458},
  year   = {2024}
}

Comments

To appear in the Journal of Noncommutative Geometry, 40 pages, v3: several minor changes

Polynomial growth and property $RD_p$ for \'etale groupoids with applications to $K$-theory

Abstract

Keywords

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