Circle correspondence $C^{\ast }$-algebras

Abstract

We investigate Cuntz-Pimsner $C^{\ast }$-algebras associated with certain correspondences of the unit circle $\mathbb{T}$. We analyze these $C^{\ast }$-algebras by analogy with irrational rotation algebras $A_{\theta }$ and Cuntz algebras ${\mathcal{O}}_n$. We construct a Rieffel type projection, study the fixed point algebras of certain actions of finite groups, and calculate the entropy of a certain endomorphism. We also study the induced map of the dual action of the gauge action on $K$-groups.

21 pages, 1 figure

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