Co-universal C*-algebras associated to aperiodic k-graphs

2011/08/18 by Sooran Kang, Kang, Sooran, Aidan Sims +1
Mathematics · #46L05 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1108.3674

openalex publication_date 2011/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a representation of each finitely aligned aperiodic k-graph Λ on the Hilbert space H^ap with basis indexed by aperiodic boundary paths in Λ. We show that the canonical expectation on B(H^ap) restricts to an expectation of the image of this representation onto the subalgebra spanned by the final projections of the generating partial isometries. We then show that every quotient of the Toeplitz algebra of the k-graph admits an expectation compatible with this one. Using this, we prove that the image of our representation, which is canonically isomorphic to the Cuntz-Krieger algebra, is co-universal for Toeplitz-Cuntz-Krieger families consisting of nonzero partial isometries.

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