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

Are Austad; Eduard Ortega; Mathias Palmstrøm

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arXiv · 2304.14458

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

Are Austad·Eduard Ortega·Mathias Palmstrøm

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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.

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BibTeX RIS

Are Austad, Eduard Ortega, Mathias Palmstrøm. 2023-04-27. Polynomial growth and property $RD_p$ for \'etale groupoids with applications to $K$-theory. https://arxiv.org/abs/2304.14458

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