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).
Qingzhai FAN
,
Xiaochun FANG
,
Xia ZHAO
. INHERITANCE OF DIVISIBILITY FORMS A LARGE SUBALGEBRA[J]. Acta mathematica scientia, Series B, 2021
, 41(1)
: 85
-96
.
DOI: 10.1007/s10473-021-0105-5
[1] Phillips N C. Large subalgebras. arXiv preprint math. OA/1408.5546v2
[2] Putnam I. F. The C*-algebras associatted with mimimal homeomorphism of the Cantor set. Pacific J Math, 1989, 136:1483-1518
[3] Lin H X, Phillips N C. Crossed products by minimal homeomorphisms. J Reine Angew Math, 2010, 641:95-122
[4] Archey D, Phillips N C. Permanence of stable rank one for centrally large subalgebra and crossed products by minimal homeomorphisms. arXiv preprint math. OA/1505.05725v1
[5] Archey D, Buck J, Phillips N C. Centrally large subalgebra and tracial Ƶ-absorbing. Int Math Res Not, 2018, 6:1857-1877
[6] Hirshberg I, Orovitz J. Tracially Ƶ-absorbing C*-algebras. J Funct Anal, 2013, 265:765-785
[7] Elliott G A, Niu Z. The C*-algebras of a minimal homeomorphism of zero mean dimensional. Duke Math J, 2017, 166:3569-3594
[8] Elliott G A, Niu Z. All irrational extended rotation algebras are AF algebras. Canadian J Math, 2014, 67:1-17
[9] Fan Q Z, Fang X C, Zhao X. Comparison properties and large subalgebra are inheritance. Rocky Mountain Journal of Mathematics, 2019, 49:1857-1867
[10] Coward K T, Elliott G A, Ivanescu C. The Cuntz semigroup as an invariant for C*-algebras. J Reine Angew Math, 2008, 623:161-193
[11] Ara P, Perera F, Toms A S. K-theory for operator algebras. Classification of C*-algebras//Aspects of Operator Algebras and Applications. Contemp Math, 534. Providence, RI:Amer Math Soc, 2011:1-71
[12] Robert L, Tikuisis A P. Nuclear dimension and Z-stability of non-simple C*-algebras. Trans Amer Math Soc, 2017, 369:4631-4670
[13] Kirchberg E, Rordam M. Divisibility properties for C*-algebras. Proc London Math Soc, 2013,106:1330- 1370
[14] Fan Q Z, Fang X C. Crossed products by finite group actions with certain tracial Rokhlin property. Acta Math Sci, 2018, 38B(2):829-842
[15] Pourgholamhossein M, Rouzbehani M, Anini M. Chain conditions for C*-algebras coming from Hilbert C*-modules. Acta Math Sci, 2018, 38B(3):1163-1173
