迹逼近可除性关于中心大子代数的遗传性

吉林大学学报(理学版) ›› 2026, Vol. 64 ›› Issue (3): 507-0510.

迹逼近可除性关于中心大子代数的遗传性

啜佩, 赵霞

重庆师范大学数学科学学院, 重庆 401331

收稿日期:2025-07-21 出版日期:2026-05-26 发布日期:2026-05-26
通讯作者: 赵霞 E-mail:xiazhao@cqnu.edu.cn

Hereditary of Tracial Approximate Divisibility for Centrally Large Subalgebras

CHUAI Pei, ZHAO Xia

School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China

Received:2025-07-21 Online:2026-05-26 Published:2026-05-26

摘要/Abstract

摘要： 在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.

关键词: 迹逼近可除性, C*-代数, 大子代数, 中心大子代数

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.

Key words: tracial approximate divisibility, C*-algebra, large subalgebra, centrally large subalgebra

中图分类号:

O177.5

啜佩, 赵霞. 迹逼近可除性关于中心大子代数的遗传性[J]. 吉林大学学报(理学版), 2026, 64(3): 507-0510.

CHUAI Pei, ZHAO Xia. Hereditary of Tracial Approximate Divisibility for Centrally Large Subalgebras[J]. Journal of Jilin University Science Edition, 2026, 64(3): 507-0510.