Constructing Menger manifold C*-diagonals in classifiable C*-algebras

Li, X. (2022) Constructing Menger manifold C*-diagonals in classifiable C*-algebras. International Mathematics Research Notices, 2022(23), pp. 18992-19053. (doi: 10.1093/imrn/rnab199)

Abstract

We initiate a detailed analysis of C*-diagonals in classifiable C*-algebras, answering natural questions concerning topological properties of their spectra and uniqueness questions. Firstly, we construct C*-diagonals with connected spectra in all classifiable stably finite C*-algebras, which are unital or stably projectionless with continuous scale. Secondly, for classifiable stably finite C*-algebras with torsion-free K0 and trivial K1⁠, we further determine the spectra of the C*-diagonals up to homeomorphism. In the unital case, the underlying space turns out to be the Menger curve. In the stably projectionless case, the space is obtained by removing a non-locally-separating copy of the Cantor space from the Menger curve. Thirdly, we show that each of our classifiable C*-algebras has continuum many pairwise non-conjugate such Menger manifold C*-diagonals.

• Item Type: Articles
• Additional Information: This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 817597).
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Li, Professor Xin
• Authors: Li, X.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: International Mathematics Research Notices
• Publisher: Oxford University Press
• ISSN: 1073-7928
• ISSN (Online): 1687-0247
• Published Online: 08 September 2021
• Copyright Holders: Copyright © 2021 The Author
• First Published: First published in International Mathematics Research Notices 2022(23): 18992-19053
• Publisher Policy: Reproduced under a Creative Commons licence