Hereditary uniform property Γ

We study the uniform property Γ for separable simple C *-algebras which have quasitraces and may not be exact. We show that a stably finite separable simple C *-algebra A with the strict comparison and uniform property Γ has tracial approximate oscillation zero and stable rank one. Moreover in this...

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Bibliographic Details
Published in:Science China. Mathematics 2023-08, Vol.66 (8), p.1813-1830
Main Author: Lin, Huaxin
Format: Article
Language:English
Subjects:
Algebra
Applications of Mathematics
Mathematics
Mathematics and Statistics
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Summary:We study the uniform property Γ for separable simple C *-algebras which have quasitraces and may not be exact. We show that a stably finite separable simple C *-algebra A with the strict comparison and uniform property Γ has tracial approximate oscillation zero and stable rank one. Moreover in this case, its hereditary C *-subalgebras also have a version of uniform property Γ. If a separable non-elementary simple amenable C *-algebra A with strict comparison has this hereditary uniform property Γ, then A is Z -stable.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-022-2005-x