Strict comparison for C*-algebras arising from almost finite groupoids

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)

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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).
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
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

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