Strict comparison for C∗ -algebras arising from almost finite groupoids
Ara P, Bonicke C, Bosa J, Li K (2020)
Publication Type: Journal article
Publication year: 2020
Journal
Book Volume: 14
Pages Range: 1692-1710
Journal Issue: 4
DOI: 10.1007/s43037-020-00079-6
Abstract
In this paper we show that for an almost finite minimal ample groupoid G, its reduced C∗-algebra Cr∗(G) has real rank zero and strict comparison even though Cr∗(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(Cr∗(G)) is almost divisible and Cu(Cr∗(G)) and Cu(Cr∗(G)⊗Z) are canonically order-isomorphic, where Z denotes the Jiang-Su algebra.
Authors with CRIS profile
Involved external institutions
Autonomous University of Barcelona (UAB) / Universitat Autònoma de Barcelona
Spain (ES)
University of Glasgow
United Kingdom (GB)
Mathematical Institute of the Polish Academy of Sciences
Poland (PL)
Spain (ES)
University of Glasgow
United Kingdom (GB)
Mathematical Institute of the Polish Academy of Sciences
Poland (PL)
How to cite
APA:
Ara, P., Bonicke, C., Bosa, J., & Li, K. (2020). Strict comparison for C∗ -algebras arising from almost finite groupoids. Banach Journal of Mathematical Analysis, 14(4), 1692-1710. https://dx.doi.org/10.1007/s43037-020-00079-6
MLA:
Ara, Pere, et al. "Strict comparison for C∗ -algebras arising from almost finite groupoids." Banach Journal of Mathematical Analysis 14.4 (2020): 1692-1710.
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