On unital absorbing extensions of C$^*$-algebras of stable rank one and real rank zero
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- by Qingnan An and Zhichao Liu;
- Proc. Amer. Math. Soc. 152 (2024), 2497-2510
- DOI: https://doi.org/10.1090/proc/16782
- Published electronically: April 25, 2024
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Abstract:
Suppose that $B$ is a separable stable $C^*$-algebra with real rank zero, stable rank one and $(\mathrm {K}_0(B), \mathrm {K}_0^+(B))$ is weakly unperforated in the sense of Elliott [Internat. J. Math. 1 (1990), no. 4, pp. 361–380]. Let $A$ be a unital simple separable nuclear $\mathrm {C}^*$-algebra. We show that $B$ has the corona factorization property and any unital extension of $A$ by $B$ is absorbing.References
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Bibliographic Information
- Qingnan An
- Affiliation: School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, People’s Republic of China
- MR Author ID: 1243373
- Email: qingnanan1024@outlook.com
- Zhichao Liu
- Affiliation: School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, People’s Republic of China
- MR Author ID: 1310448
- Email: lzc.12@outlook.com
- Received by editor(s): March 13, 2023
- Received by editor(s) in revised form: October 20, 2023
- Published electronically: April 25, 2024
- Additional Notes: The first author was supported by NNSF of China (No.:12101113) and the Fundamental Research Funds for the Central Universities (No.:2412021QD001).
The second author was supported by NNSF of China (Nos.:12101102, 12071109) and the Fundamental Research Funds for the Central Universities (No.: DUT20RC(3)064).
The second author is the corresponding author - Communicated by: Matthew Kennedy
- © Copyright 2024 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 152 (2024), 2497-2510
- MSC (2020): Primary 46L80; Secondary 19K33, 46L35
- DOI: https://doi.org/10.1090/proc/16782