迹逼近可除性关于中心大子代数的遗传性

Hereditary of Tracial Approximate Divisibility for Centrally Large Subalgebras

摘要

在 $\mathrm{C}^{*}$ -代数无可分条件的情形下，基于迹逼近可除的定义，利用中心大子代数的结构性质，证明迹逼近可除性关于中心大子代数具有遗传性。设A是一无限维有单位元的单 $\mathrm{C}^{*}$ -代数， B是A的中心大子代数，若 B 有迹逼近可除性，则 A 也有迹逼近可除性。

Abstract

Without the separability condition for $C^{*}$ -algebras，based on the definition of tracial approximate divisibility，and by employing the structural properties of centrally large subalgebras，we prove that tracial approximate divisibility is hereditary with respect to centrally large subalgebras．Let A be an infinite dimensional unital simple $C^{*}$ -algebra and B be a centrally large subalgebra of A．If B has tracial approximate divisibility，then A also has tracial approximate divisibility．

关键词

迹逼近可除性 / C^*-代数 / 大子代数 / 中心大子代数

Key words

tracial approximate divisibility / C^*-algebra / large subalgebra / centrally large subalgebra

参考文献

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基金资助

国家自然科学基金(12201090)

重庆市自然科学基金(CSTB2022NSCQ-MSX1024)

重庆市教育委员会科学技术研究项目(KJQN202200535)