K-theory invariance of $L^p$-operator algebras associated with \'etale groupoids of strong subexponential growth

Are Austad; Eduard Ortega; Mathias Palmstrøm

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arXiv · 2410.05005

K-theory invariance of $L^p$-operator algebras associated with \'etale groupoids of strong subexponential growth

Are Austad·Eduard Ortega·Mathias Palmstrøm

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Abstract

We introduce the notion of (strong) subexponential growth for \'etale groupoids and study its basic properties. In particular, we show that the K-groups of the associated groupoid $L^p$-operator algebras are independent of $p \in [1,\infty)$ whenever the groupoid has strong subexponential growth. Several examples are discussed. Most significantly, we apply classical tools from analytic number theory to exhibit an example of an \'etale groupoid associated with a shift of infinite type which has strong subexponential growth, but not polynomial.

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BibTeX RIS

Are Austad, Eduard Ortega, Mathias Palmstrøm. 2024-10-07. K-theory invariance of $L^p$-operator algebras associated with \'etale groupoids of strong subexponential growth. https://arxiv.org/abs/2410.05005

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