用表示法表征可嵌入 AF 的 $$C^*$-gebras

IF 0.6 3区数学 Q3 MATHEMATICS

Acta Mathematica Hungarica Pub Date : 2024-06-08 DOI:10.1007/s10474-024-01442-x

Y. Liu

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引用次数: 0

摘要

AF-嵌入的一个主要未决问题是，是否每个可分离的精确准对边 $C^*$- 代数都可以嵌入到一个 AF- 代数中。在本文中，我们通过表示法描述了可AF嵌入的$C^*$-代数的特征，以观察它们与可分离的精确准对角$C^*$-代数的相似性。作为应用，我们证明了当且仅当可分离精确准对角$C^*$-代数的每个忠实本质表示都是某种$*$-表示时，每个可分离精确准对角$C^*$-代数都是可AF-嵌入的。我们还证明，当且仅当一个可分离的（C^*\）-代数可以嵌入到一个特定的（C^*\）-代数中时，它才是可嵌入的。

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Characterizing AF-embeddable $C^*$-algebras by representations

A major open problem of AF-embedding is whether every separable exact quasidiagonal $C^*$-algebra can be embedded into an AF-algebra. In this paper we characterize AF-embeddable $C^*$-algebras by representations to observe their similarity to the separable exact quasidiagonal $C^*$-algebras. As an application, we show that every separable exact quasidiagonal $C^*$-algebra is AF-embeddable if and only if every faithful essential representation of a separable exact quasidiagonal $C^*$-algebra is a certain kind of $*$-representation. We also show that a separable $C^*$-algebra is AF-embeddable if and only if it can be embedded into a particular $C^*$-algebra.

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来源期刊

Acta Mathematica Hungarica 数学-数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

4-8 weeks

期刊介绍： Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.