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 $X$.

28 pages. This is a slightly updated version of a preprint from 2004. Submitted for publication. In version 2 the Introduction has been changed, two remarks (Remark 7.6 and 7.7) have been added and the list of references has been updated

References in corpus (3)

• A construction of $C^{\ast }$-algebras from $C^{\ast }$-correspondences
• C*-crossed products and shift spaces
• On C*-algebras Associated with Sofic Shifts

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