CO-UNIVERSAL C*-ALGEBRAS ASSOCIATED TO APERIODIC k-GRAPHS

KANG, SOORAN ; SIMS, AIDAN

Glasgow mathematical journal, Tome 56 (2014) no. 3, pp. 537-550

Résumé

We construct a representation of each finitely aligned aperiodic k-graph Λ on the Hilbert space $\mathcal{H}^{\rm ap}$ with basis indexed by aperiodic boundary paths in Λ. We show that the canonical expectation on $\mathcal{B}(\mathcal{H}^{\rm ap})$ 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.

Détail

DOI : 10.1017/S001708951300044X

Mots-clés : Primary 46L05

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