C-algebras from Anzai Flows and Their K-groups
نویسندگان
چکیده
We study the C∗-algebra An,θ generated by the Anzai flow on the n-dimensional torus T. It is proved that this algebra is a simple quotient of the group C∗-algebra of a lattice subgroup Dn of a (n + 2)-dimensional connected simply connected nilpotent Lie group Fn whose corresponding Lie algebra is the generic filiform Lie algebra fn. Other simple infinite dimensional quotients of C∗(Dn) are also characterized and represented as matrix algebras over simple affine Furstenberg transformation group C∗-algebras of the lower dimensional tori. The Kgroups of theAn,θ and other simple quotients of C ∗(Dn) are studied, the Pimsner-Voiculescu 6-term exact sequence being a useful tool. The rank of the K-groups of An,θ is studied as explicitly as possible, and is proved to be the same as for more general transformation group C∗-algebras of T including the Furstenberg transformation group C∗-algebras AFf,θ . An error (about these K-groups) in the literature is addressed.
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