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# The Ideal Structures of Crossed Products of Cuntz Algebras by Quasi-Free Actions of Abelian Groups

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Published:2003-12-01
Printed: Dec 2003
• Takeshi Katsura
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## Abstract

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.
 MSC Classifications: 46L05 - General theory of $C^*$-algebras 46L55 - Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20] 46L45 - Decomposition theory for $C^*$-algebras

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