Ara, P., Bonicke, C. , Bosa, J. and Li, K. (2020) Strict comparison for C*-algebras arising from almost finite groupoids. Banach Journal of Mathematical Analysis, 14, pp. 1692-1710. (doi: 10.1007/s43037-020-00079-6)
Text
218436.pdf - Accepted Version 557kB |
Abstract
In this paper we show that for an almost finite minimal ample groupoid G, its reduced C∗-algebra C∗r(G) has real rank zero and strict comparison even though C∗r(G) may not be nuclear in general. Moreover, if we further assume G being also second countable and non-elementary, then its Cuntz semigroup Cu(C∗r(G)) is almost divisible and Cu(C∗r(G)) and Cu(C∗r(G)⊗Z) are canonically order-isomorphic, where Z denotes the Jiang-Su algebra.
Item Type: | Articles |
---|---|
Additional Information: | The first and third authors were partially supported by the DGI-MINECO and European Regional Development Fund, jointly, through the grant MTM2017-83487-P. Also, they acknowledge support from the Generalitat de Catalunya through the grant 2017-SGR-1725. The second author was partially supported by Deutsche Forschungsgemeinschaft (SFB 878) and the Alexander von Humboldt Foundation. The third author is also supported by Beatriu de Pinós programme (BP-2017-0079). The fourth author has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 677120-INDEX). |
Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Bonicke, Dr Christian |
Authors: | Ara, P., Bonicke, C., Bosa, J., and Li, K. |
College/School: | College of Science and Engineering > School of Mathematics and Statistics |
Journal Name: | Banach Journal of Mathematical Analysis |
Publisher: | Springer |
ISSN: | 2662-2033 |
ISSN (Online): | 1735-8787 |
Published Online: | 24 June 2020 |
Copyright Holders: | Copyright © 2020 Tusi Mathematical Research Group (TMRG) |
First Published: | First published in Banach Journal of Mathematical Analysis 14:1692-1710 |
Publisher Policy: | Reproduced in accordance with the publisher copyright policy |
University Staff: Request a correction | Enlighten Editors: Update this record