Amenability of groupoids arising from partial semigroup actions and topological higher rank graphs
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- by Jean N. Renault and Dana P. Williams PDF
- Trans. Amer. Math. Soc. 369 (2017), 2255-2283 Request permission
Abstract:
We consider the amenability of groupoids $G$ equipped with a group valued cocycle $c:G\to Q$ with amenable kernel $c^{-1}(e)$. We prove a general result which implies, in particular, that $G$ is amenable whenever $Q$ is amenable and if there is countable set $D\subset G$ such that $c(G^{u})D=Q$ for all $u\in G^{(0)}$.
We show that our result is applicable to groupoids arising from partial semigroup actions. We explore these actions in detail and show that these groupoids include those arising from directed graphs, higher rank graphs and even topological higher rank graphs. We believe our methods yield a nice alternative groupoid approach to these important constructions.
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Additional Information
- Jean N. Renault
- Affiliation: Départment de Mathématiques, Université d’Orléans et CNRS (UMR 7349 et FR 2964), 45067 Orléans Cedex 2, France
- MR Author ID: 146950
- Email: jean.renault@univ-orleans.fr
- Dana P. Williams
- Affiliation: Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755-3551
- MR Author ID: 200378
- Email: dana.williams@Dartmouth.edu
- Received by editor(s): January 12, 2015
- Received by editor(s) in revised form: March 17, 2015
- Published electronically: April 8, 2016
- Additional Notes: The second author was supported by a grant from the Simons Foundation.
- © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 2255-2283
- MSC (2010): Primary 22A22, 46L55, 46L05
- DOI: https://doi.org/10.1090/tran/6736
- MathSciNet review: 3592511