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Cartan subalgebras in uniform Roe algebras

Abstract:
In this paper we study structural and uniqueness questions for Cartan subalgebras of uniform Roe algebras. We characterise when an inclusion B⊆A of C∗-algebras is isomorphic to the canonical inclusion of ℓ∞(X) inside a uniform Roe algebra C∗u(X) associated to a metric space of bounded geometry. We obtain uniqueness results for “Roe Cartans” inside uniform Roe algebras up to automorphism when X coarsely embeds into Hilbert space, and up to inner automorphism when X has property A.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.4171/GGD/570

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Institution:
University of Oxford
Department:
Mathematical Institute
Oxford college:
St John's College
Role:
Author
ORCID:
0000-0003-2264-8943
Publisher:
European Mathematical Society
Journal:
Groups, Geometry, and Dynamics More from this journal
Volume:
14
Issue:
3
Pages:
949–989
Publication date:
2020-10-21
Acceptance date:
2019-05-20
DOI:
EISSN:
1661-7215
ISSN:
1661-7207
Language:
English
Keywords:
Pubs id:
pubs:1050048
UUID:
uuid:b85036f3-5c59-4fca-b0ff-6257c448dbd0
Local pid:
pubs:1050048
Source identifiers:
1050048
Deposit date:
2019-09-07

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