Cuntz-Pimsner C*-algebras associated with subshifts

Abstract

By using C*-correspondences and Cuntz-Pimsner algebras, we associate to every subshift (also called a shift space) $X$ a C*-algebra $O_X$, which is a generalization of the Cuntz-Krieger algebras. We show that $O_X$ is the universal C*-algebra generated by partial isometries satisfying relations given by $X$. We also show that $O_X$ is a one-sided conjugacy invariant of $X$.