INHERITANCE OF DIVISIBILITY FORMS A LARGE SUBALGEBRA

doi:10.1007/s10473-021-0105-5

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (1): 85-96.doi: 10.1007/s10473-021-0105-5

INHERITANCE OF DIVISIBILITY FORMS A LARGE SUBALGEBRA

范庆斋¹, 方小春², 赵霞²

1. Department of Mathematics Shanghai Maritime University, Shanghai 201306, China;
2. Department of Mathematics Tongji University, Shanghai 200092, China

收稿日期:2019-11-14 修回日期:2020-02-21 出版日期:2021-02-25 发布日期:2021-04-06
作者简介:Qingzhai FAN,E-mail:qzfan@shmtu.edu.cn;Xiaochun FANG,E-mail:xfang@mail.tongji.edu.cn;Xia ZHAO,E-mail: 1710383@tongji.edu.cn
基金资助:
The research of first author was supported by National Natural Sciences Foundation of China (11501357, 11571008). The research of the second author was supported by National Natural Sciences Foundation of China (11871375).

INHERITANCE OF DIVISIBILITY FORMS A LARGE SUBALGEBRA

Qingzhai FAN¹, Xiaochun FANG², Xia ZHAO²

1. Department of Mathematics Shanghai Maritime University, Shanghai 201306, China;
2. Department of Mathematics Tongji University, Shanghai 200092, China

Received:2019-11-14 Revised:2020-02-21 Online:2021-02-25 Published:2021-04-06
About author:Qingzhai FAN,E-mail:qzfan@shmtu.edu.cn;Xiaochun FANG,E-mail:xfang@mail.tongji.edu.cn;Xia ZHAO,E-mail: 1710383@tongji.edu.cn
Supported by:
The research of first author was supported by National Natural Sciences Foundation of China (11501357, 11571008). The research of the second author was supported by National Natural Sciences Foundation of China (11871375).

摘要/Abstract

摘要： Let $A$ be an infinite dimensional stably finite unital simple separable ${\rm C^*}$-algebra. Let $B\subset A$ be a stably (centrally) large subalgebra in $A$ such that $B$ is $m$-almost divisible ($m$-almost divisible, weakly $(m,n)$-divisible). Then $A$ is $2(m+1)$-almost divisible (weakly $m$-almost divisible, secondly weakly $(m,n)$-divisible).

关键词: C^*-algebras, large subalgebra, Cuntz semigroup

Abstract: Let $A$ be an infinite dimensional stably finite unital simple separable ${\rm C^*}$-algebra. Let $B\subset A$ be a stably (centrally) large subalgebra in $A$ such that $B$ is $m$-almost divisible ($m$-almost divisible, weakly $(m,n)$-divisible). Then $A$ is $2(m+1)$-almost divisible (weakly $m$-almost divisible, secondly weakly $(m,n)$-divisible).

Key words: C^*-algebras, large subalgebra, Cuntz semigroup

中图分类号:

46L35

范庆斋, 方小春, 赵霞. INHERITANCE OF DIVISIBILITY FORMS A LARGE SUBALGEBRA[J]. 数学物理学报(英文版), 2021, 41(1): 85-96.

Qingzhai FAN, Xiaochun FANG, Xia ZHAO. INHERITANCE OF DIVISIBILITY FORMS A LARGE SUBALGEBRA[J]. Acta mathematica scientia,Series B, 2021, 41(1): 85-96.

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INHERITANCE OF DIVISIBILITY FORMS A LARGE SUBALGEBRA

INHERITANCE OF DIVISIBILITY FORMS A LARGE SUBALGEBRA

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