Article contents
Tracial approximation in simple
${C}^{\ast }$-algebras
Published online by Cambridge University Press: 26 February 2021
Abstract
We revisit the notion of tracial approximation for unital simple
$C^*$
-algebras. We show that a unital simple separable infinite dimensional
$C^*$
-algebra A is asymptotically tracially in the class of
$C^*$
-algebras with finite nuclear dimension if and only if A is asymptotically tracially in the class of nuclear
$\mathcal {Z}$
-stable
$C^*$
-algebras.
MSC classification
- Type
- Article
- Information
- Copyright
- © Canadian Mathematical Society 2021
Footnotes
Huaxin Lin is the corresponding author.
Xuanlong Fu was supported by China Postdoctoral Science Foundation, grant # 2020M670962, and partially supported by an NSFC grant (NSFC 11420101001). Huaxin Lin was partially supported by an NSF grant (DMS-1954600). Both authors acknowledge the support from the Research Center of Operator Algebras at East China Normal University which is partially supported by Shanghai Key Laboratory of PMMP, Science and Technology Commission of Shanghai Municipality (STCSM), grant #13dz2260400 and a NNSF grant (11531003).
References
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