Divisible Properties for Asymptotically Tracially Approximation of C*-algebras

Qingzhai Fan , Jiahui Wang

Chinese Annals of Mathematics, Series B ›› 2025, Vol. 46 ›› Issue (5) : 695 -712.

PDF
Chinese Annals of Mathematics, Series B ›› 2025, Vol. 46 ›› Issue (5) : 695 -712. DOI: 10.1007/s11401-025-0034-z
Article
research-article

Divisible Properties for Asymptotically Tracially Approximation of C*-algebras

Author information +
History +
PDF

Abstract

The authors show that ra-almost divisibility and weak (m, n)-divisibility of C*-algebras in a class $\cal{P}$ are preserved to the simple unital C*-algebras which are asymptotically tracially in $\cal{P}$.

Keywords

C*-algebras / Asymptotically tracially approximation / Cuntz semigroup / 46L35 / 46L05 / 46L80

Cite this article

Download citation ▾
Qingzhai Fan, Jiahui Wang. Divisible Properties for Asymptotically Tracially Approximation of C*-algebras. Chinese Annals of Mathematics, Series B, 2025, 46(5): 695-712 DOI:10.1007/s11401-025-0034-z

登录浏览全文

4963

注册一个新账户 忘记密码

References

[1]

ElliottG A. On the classification of inductive limits of sequences of semisimple finite dimensional algebras. J. Algebra, 1976, 38: 29-44.

[2]

ElliottG A, GongG H. On the classification of C*-algebras of real rank zero, II. Ann. Math., 1996, 144: 497-610.

[3]

ElliottG A, GongG H, LiL Q. On the classification of simple inductive limit C*-algebras II: The isomorphism theorem. Invent. Math., 2007, 168: 249-320.

[4]

GongG H. On the classification of simple inductive limit C*-algebras. I: The reduction theorem. Doc. Math., 2002, 7: 255-461.

[5]

LinH X. Tracially AF C*-algebras. Trans. Amer. Math. Soc., 2001, 353: 683-722

[6]

LinH X. The tracial topological rank of C*-algebras. Proc. London Math. Soc., 2001, 83: 199-234.

[7]

GongG H, LinH X, NiuZ. Classification of finite simple amenable $\cal{Z}$-stable C*-algebras, I: C*-algebra with generalized tracial rank one. C. R. Math. Rep. Acad. Sci. Canada, 2020, 42: 63-450

[8]

GongG H, LinH X, NiuZ. Classification of finite simple amenable $\cal{Z}$-stable C*-algebras, II: C*-algebras with rational generalized tracial rank one. C. R. Math. Rep. Acad. Sci. Canada, 2020, 42: 451-539

[9]

Elliott, G. A., Gong, G. H., Lin, H. X. and Niu, Z., On the classification of simple amenable C*-algebras with finite decomposition rank, II, arXiv: 1507.03437.

[10]

TikuisisA, WhiteS, WinterW. Quasidiagonality of nuclear C*-algebras. Ann. Math., 2017, 185: 229-284.

[11]

HirshbergI, OrovitzJ. Tracially $\cal{Z}$-absorbing C*-algebras. J. Funct. Anal., 2013, 265: 765-785.

[12]

ElliottG A, GongG H, LinH X, NiuZ. Simple stably projectionless C*-algebras with generalized tracial rank one. J. Noncommut. Geom., 2020, 14: 251-347.

[13]

Gong, G. H. and Lin, H. X., On classification of non-unital simple amenable C*-algebras, II, Journal of Geometry and Physics, 158, 2020, Article 103865, 102 pp.

[14]

Gong, G. H. and Lin, H. X., On classification of non-unital simple amenable C*-algebras, III, arXiv: 2010.01788.

[15]

FuX L, LinH X. Tracial approximation in simple C*-algebras. Canad. J. Math., 2021, 26: 1-63

[16]

FanQ Z, FangX C. Comparison properties for asymptotically tracially approximation C*-algebras. Acta Math. Sin. Engl. Series, 2023, 39: 863-884.

[17]

RobertL, TikuisisA. Nuclear dimension and $\cal{Z}$-stability of non-simple C*-algebras. Trans. Amer. Math. Soc., 2017, 369: 4631-4670.

[18]

RobertL, RørdamM. Divisibility properties for C*-algelbras. Proc. London Math. Soc., 2013, 106: 1330-1370.

[19]

CuntzJ. Dimension functions on simple C*-algebras. Math. Ann., 1978, 233: 145-153.

[20]

CowardK T, ElliottG A, IvanescuC. The Cuntz semigroup as an invariant for C*-algebras. J. Reine Angew. Math., 2008, 623: 161-193

[21]

Antoine, R., Perera, F. and Thiel, H., Tensor products and regularity properties of Cuntz semigroups, Mem. Amer. Math. Soc., 251 (1199), 2018, 199 pp.

[22]

AntoineR, PereraF, RobertL, ThielH. C*-algebras of stable rank one and their Cuntz semigroups. Duke Math. J., 2022, 171: 33-99.

[23]

ElliottG A, FanQ Z, FangX C. Certain properties of tracial approximation C*-algebras. C. R. Math. Rep. Acad. Sci. Canada, 2018, 40: 104-133

RIGHTS & PERMISSIONS

The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg

AI Summary AI Mindmap
PDF

77

Accesses

0

Citation

Detail

Sections
Recommended

AI思维导图

/