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Projections in some simple $ C\sp \ast$-crossed products

Authors: Ja A Jeong and Gie-Hyun Park
Journal: Proc. Amer. Math. Soc. 123 (1995), 3317-3321
MSC: Primary 46L05; Secondary 46L55
MathSciNet review: 1249884
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Abstract: Let $ \alpha $ be an outer action by a finite group G on a simple $ {C^ \ast }$-algebra A. If each hereditary $ {C^ \ast }$-subalgebra of A has an approximate identity consisting of projections, then every hereditary $ {C^ \ast }$-subalgebra of the crossed product $ A{ \times _\alpha }G$ has a projection.

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  • [1] B. E. Blackadar, Comparison theory for simple $ {C^ \ast }$-algebras, Operator algebras and applications, Vol. 1, London Math. Soc. Lecture Note Ser., vol. 135, Cambridge Univ. Press, Cambridge and New York, 1988, pp. 21-54.
  • [2] B. E. Blackadar and J. Cuntz, The structure of stable algebraically simple $ {C^ \ast }$-algebras, Amer. J. Math. 104 (1982), 813-822. MR 667536 (84c:46057)
  • [3] B. E. Blackadar and A. Kumjian, Skew products of relations and structure of simple $ {C^ \ast }$-algebras, Math. Z. 189 (1985), 55-63. MR 776536 (86g:46083)
  • [4] L. G. Brown and G. K. Pedersen, $ {C^ \ast }$-algebras of real rank zero, J. Funct. Anal. 99 (1991), 131-149. MR 1120918 (92m:46086)
  • [5] G. A. Elliott, Some simple $ {C^ \ast }$-algebras constructed as crossed products with discrete outer automorphism groups, Res. Inst. Math. Sci. 16 (1980), 299-311. MR 574038 (81j:46102)
  • [6] -, A classification of certain simple $ {C^ \ast }$-algebras, preprint.
  • [7] A. Kishimoto, Outer automorphisms and reduced crossed products, Comm. Math. Phys. 81 (1981), 429-435. MR 634163 (83c:46061)
  • [8] J. Rosenberg, Appendix to O. Bratteli's paper on "crossed products of UHF-algebras", Duke Math. J. 46 (1979), 25-26. MR 523599 (82a:46064)
  • [9] M. Rørdam, On the structure of simple $ {C^ \ast }$-algebras tensored with a UHF-algebra, J. Funct. Anal. 100 (1991), 1-17. MR 1124289 (92m:46091)
  • [10] S. Zhang, A property of purely infinite simple $ {C^ \ast }$-algebras, Proc. Amer. Math. Soc. 109 (1990), 717-720. MR 1010004 (90k:46134)
  • [11] -, Certain $ {C^ \ast }$-algebras with real rank zero and their corona and multiplier algebras, Part I, Pacific J. Math. 155 (1992), 169-197. MR 1174483 (94i:46093)

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Article copyright: © Copyright 1995 American Mathematical Society

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