Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (1): 85-96.doi: 10.1007/s10473-021-0105-5

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INHERITANCE OF DIVISIBILITY FORMS A LARGE SUBALGEBRA

Qingzhai FAN1, Xiaochun FANG2, Xia ZHAO2   

  1. 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).

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

CLC Number: 

  • 46L35
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