Polynomial growth and property $RD_p$ for étale groupoids with applications to $K$-theory
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911783279656960 |
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| author | Austad, Are Ortega, Eduard Palmstrøm, Mathias |
| author_facet | Austad, Are Ortega, Eduard Palmstrøm, Mathias |
| contents | We investigate property $RD_p$ for étale 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2304_14458 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Polynomial growth and property $RD_p$ for étale groupoids with applications to $K$-theory Austad, Are Ortega, Eduard Palmstrøm, Mathias Operator Algebras Functional Analysis K-Theory and Homology 46L80, 47L10, 46L87 We investigate property $RD_p$ for étale 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. |
| title | Polynomial growth and property $RD_p$ for étale groupoids with applications to $K$-theory |
| topic | Operator Algebras Functional Analysis K-Theory and Homology 46L80, 47L10, 46L87 |
| url | https://arxiv.org/abs/2304.14458 |