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

Journal Article


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Abstract


  • We construct a representation of each finitely aligned aperiodic k-graph Λ on the Hilbert space with basis indexed by aperiodic boundary paths in Λ. We show that the canonical expectation on 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.

UOW Authors


Publication Date


  • 2014

Citation


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

Scopus Eid


  • 2-s2.0-84907334981

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=4254&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/3238

Number Of Pages


  • 13

Start Page


  • 537

End Page


  • 550

Volume


  • 56

Issue


  • 3

Abstract


  • We construct a representation of each finitely aligned aperiodic k-graph Λ on the Hilbert space with basis indexed by aperiodic boundary paths in Λ. We show that the canonical expectation on 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.

UOW Authors


Publication Date


  • 2014

Citation


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

Scopus Eid


  • 2-s2.0-84907334981

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=4254&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/3238

Number Of Pages


  • 13

Start Page


  • 537

End Page


  • 550

Volume


  • 56

Issue


  • 3