Volume 19, Issue 1 (4-2024)                   IJMSI 2024, 19(1): 51-62 | Back to browse issues page


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Jamali S. Tracial Cyclic Rokhlin Property for Automorphisms of Non-unital Simple C*-algebras. IJMSI 2024; 19 (1) :51-62
URL: http://ijmsi.ir/article-1-1372-en.html
Abstract:  
The tracial cyclic Rokhlin property for automorphisms of simple not necessarily unital C*-algebras is investigated. We show that the tracial cyclic Rokhlin property is preserved by going to certain restrictions to subalgebras and taking direct limit or tensor products of actions. We also show that under certain conditions properties such as real rank zero, the tracial rank zero, stable rank one, (tracial) Z-stability, Property (SP), strict comparison on projections are passed to crossed products under automorphisms with the tracial cyclic Rokhlin property.
Type of Study: Research paper | Subject: General

References
1. 1. M. Amini, N. Golestani, S. Jamali, N. C. Phillips, Simple Tracially Z-absorbing C*-algebras, under preparation.
2. B. Blackadar, The Stable Rank of Full Corners in C*-algebras, Proc. Amer. Math. Soc., 132, (2004), 2945-2950. [DOI:10.1090/S0002-9939-04-07148-5]
3. L. G. Brown, G. K. Pedersen, C*-algebras of Real Rank Zero, J. Funct. Anal., 99, (1991), 131-149. [DOI:10.1016/0022-1236(91)90056-B]
4. G. A. Elliott, G. Gong, H. Lin, Z. Niu, Simple Stably Projectionless C*-algebras with Generalized Tracial Rank One, arXiv:1711.01240, 2017.
5. M. Forough, N. Golestani, Tracial Rokhlin Property for Finite Group Action on Nonunital Simpe C*-algebras, arXiv:1711.10818v1, 2017.
6. I. Hirshberg, J. Orovitz, Tracially Z-absorbing C*-algebras, J. Func. Anal., 265, (2013), 765-785. [DOI:10.1016/j.jfa.2013.05.005]
7. V. Kaftal, P. W. Ng, S. Zhang, Commutators and Linear Spans of Projections in Certain Finite C*-algebras, J. Funct. Anal., 266, (2014), 1883-1912. [DOI:10.1016/j.jfa.2013.12.009]
8. A. Kishimoto, Outer Automorphisms and Reduced Crossed Products of Simple C*-algebras, Commun. Math. Phys., 81, (1981), 429-435. [DOI:10.1007/BF01209077]
9. H. Lin, The Rokhlin Property for Automorphisms on Simple C*-algebras, arXiv:math/0602513, 2010.
10. H. Lin, Z. Niu, Lifting KK-elements, Asymptotic Unitary Equivalence and Classification of Simple C*-algebras, Adv. Math., 219, (2008), 1729-1769. [DOI:10.1016/j.aim.2008.07.011]
11. H. Lin, H. Osaka, The Rokhlin Property and the Tracial Topological Rank, J. Funct. Anal., 218, (2005), 475-494. [DOI:10.1016/j.jfa.2004.05.005]
12. H. Lin, H. Osaka, Tracial Rokhlin Property for Automorphisms on Simple AT-algebras, Ergod. Theory Dyn. Syst., 28, (2008), 1215-1241. [DOI:10.1017/S0143385707000764]
13. H. Matui, Z-Actions on AH-Algebras and Z2-Actions on AF Algebras, Comm. Math. Phys., 297, (2010), 529-551. [DOI:10.1007/s00220-009-0969-z]
14. N. C. Phillips, The Tracial Rokhlin Property for Actions of Finite Groups on C*-algebras, Amer. J. Math., 133(3), (2011), 581-636. [DOI:10.1353/ajm.2011.0016]
15. N. C. Phillips, An Introduction to Crossed Product C*-algebras and Minimal Dynamics, preprint, 2017.
16. N. C. Phillips, H. Osaka, Stable and Real Rank for Crossed Products by Automorphisms with the Tracial Rokhlin Property, Ergod. Theory Dyn. Syst., 26, (2006), 1579-1621. [DOI:10.1017/S0143385706000265]
17. Y. Sato, Actions of Amenable Groups and Crossed Products of Z-absorbing C*-algebras, arXiv:1612.08529.
18. A. S. Toms, W. Winter, Strongly Self-absorbing C*-algebras, Trans. Amer. Math. Soc., 359, (2007), 3999-4029. [DOI:10.1090/S0002-9947-07-04173-6]
19. W. Winter, J. Zacharias, The Nuclear Dimension of C*-algebras, Adv. Math., 224, (2010), 461-498. [DOI:10.1016/j.aim.2009.12.005]

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