Co-universal c∗-algebras associated to aperiodic k-graphs

Authors

Sooran Kang, University of OtagoFollow
Aidan Sims, University of WollongongFollow

RIS ID

92799

Publication Details

Kang, S. & Sims, A. (2014). Co-universal c∗-algebras associated to aperiodic k-graphs. Glasgow Mathematical Journal, 56 (3), 537-550.

Abstract

We construct a representation of each finitely aligned aperiodic k-graph Λ on the Hilbert space H^apwith 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 non-zero partial isometries.