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.Kishimotoʹs 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.