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Search: MSC category 46L45 ( Decomposition theory for $C^$-algebras *$-algebras * )

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1. CJM 2003 (vol 55 pp. 1302)

Katsura, Takeshi
The Ideal Structures of Crossed Products of Cuntz Algebras by Quasi-Free Actions of Abelian Groups
We completely determine the ideal structures of the crossed products of Cuntz algebras by quasi-free actions of abelian groups and give another proof of A.~Kishimoto's result on the simplicity of such crossed products. We also give a necessary and sufficient condition that our algebras become primitive, and compute the Connes spectra and $K$-groups of our algebras.

Categories:46L05, 46L55, 46L45

2. CJM 1998 (vol 50 pp. 323)

Dykema, Kenneth J.; Rørdam, Mikael
Purely infinite, simple $C^\ast$-algebras arising from free product constructions
Examples of simple, separable, unital, purely infinite $C^\ast$-algebras are constructed, including: \item{(1)} some that are not approximately divisible; \item{(2)} those that arise as crossed products of any of a certain class of $C^\ast$-algebras by any of a certain class of non-unital endomorphisms; \item{(3)} those that arise as reduced free products of pairs of $C^\ast$-algebras with respect to any from a certain class of states.

Categories:46L05, 46L45

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