Projections in some simple 𝐶*-crossed products

Jeong, Ja A; Park, Gie-Hyun

doi:10.1090/S0002-9939-1995-1249884-6

Projections in some simple $C^ \ast$-crossed products
HTML articles powered by AMS MathViewer

by Ja A Jeong and Gie-Hyun Park

Proc. Amer. Math. Soc. 123 (1995), 3317-3321

DOI: https://doi.org/10.1090/S0002-9939-1995-1249884-6

PDF | Request permission

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.

References

Comparison theory for simple

algebras, Operator algebras and applications

Bruce E. Blackadar and Joachim Cuntz, The structure of stable algebraically simple $C^{\ast }$-algebras, Amer. J. Math. 104 (1982), no. 4, 813–822. MR 667536, DOI 10.2307/2374206
Bruce Blackadar and Alexander Kumjian, Skew products of relations and the structure of simple $C^\ast$-algebras, Math. Z. 189 (1985), no. 1, 55–63. MR 776536, DOI 10.1007/BF01246943
Lawrence G. Brown and Gert K. Pedersen, $C^*$-algebras of real rank zero, J. Funct. Anal. 99 (1991), no. 1, 131–149. MR 1120918, DOI 10.1016/0022-1236(91)90056-B
George A. Elliott, Some simple $C^{\ast }$-algebras constructed as crossed products with discrete outer automorphism groups, Publ. Res. Inst. Math. Sci. 16 (1980), no. 1, 299–311. MR 574038, DOI 10.2977/prims/1195187509

A classification of certain simple

algebras

Akitaka Kishimoto, Outer automorphisms and reduced crossed products of simple $C^{\ast }$-algebras, Comm. Math. Phys. 81 (1981), no. 3, 429–435. MR 634163, DOI 10.1007/BF01209077
Jonathan Rosenberg, Appendix to: “Crossed products of UHF algebras by product type actions” [Duke Math. J. 46 (1979), no. 1, 1–23; MR 82a:46063 above] by O. Bratteli, Duke Math. J. 46 (1979), no. 1, 25–26. MR 523599
Mikael Rørdam, On the structure of simple $C^*$-algebras tensored with a UHF-algebra, J. Funct. Anal. 100 (1991), no. 1, 1–17. MR 1124289, DOI 10.1016/0022-1236(91)90098-P
Shuang Zhang, A property of purely infinite simple $C^*$-algebras, Proc. Amer. Math. Soc. 109 (1990), no. 3, 717–720. MR 1010004, DOI 10.1090/S0002-9939-1990-1010004-X
Shuang Zhang, Certain $C^\ast$-algebras with real rank zero and their corona and multiplier algebras. I, Pacific J. Math. 155 (1992), no. 1, 169–197. MR 1174483, DOI 10.2140/pjm.1992.155.169