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Twisted k-graph algebras associated to Bratteli diagrams

Journal Article


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Abstract


  • © 2015 Springer Basel Given a system of coverings of k-graphs, we show that the second cohomology of the resulting (k + 1)-graph is isomorphic to that of any one of the k-graphs in the system, and compute the semifinite traces of the resulting twisted (k + 1)-graph C*-algebras. We then consider Bratteli diagrams of 2-graphs whose twisted C*-algebras are matrix algebras over noncommutative tori. For such systems we calculate the ordered K-theory of the resulting twisted 3-graph C*-algebras. We deduce that every such C*-algebra is Morita equivalent to the C*-algebra of a rank-2 Bratteli diagram in the sense of Pask–Raeburn–Rørdam–Sims.

Publication Date


  • 2015

Citation


  • Pask, D. A., Sierakowski, A. & Sims, A. D. (2015). Twisted k-graph algebras associated to Bratteli diagrams. Integral Equations and Operator Theory, 81 (3), 375-408. Integral Equations and Operator Theory

Scopus Eid


  • 2-s2.0-84925537030

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=4772&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/3753

Number Of Pages


  • 33

Start Page


  • 375

End Page


  • 408

Volume


  • 81

Issue


  • 3

Abstract


  • © 2015 Springer Basel Given a system of coverings of k-graphs, we show that the second cohomology of the resulting (k + 1)-graph is isomorphic to that of any one of the k-graphs in the system, and compute the semifinite traces of the resulting twisted (k + 1)-graph C*-algebras. We then consider Bratteli diagrams of 2-graphs whose twisted C*-algebras are matrix algebras over noncommutative tori. For such systems we calculate the ordered K-theory of the resulting twisted 3-graph C*-algebras. We deduce that every such C*-algebra is Morita equivalent to the C*-algebra of a rank-2 Bratteli diagram in the sense of Pask–Raeburn–Rørdam–Sims.

Publication Date


  • 2015

Citation


  • Pask, D. A., Sierakowski, A. & Sims, A. D. (2015). Twisted k-graph algebras associated to Bratteli diagrams. Integral Equations and Operator Theory, 81 (3), 375-408. Integral Equations and Operator Theory

Scopus Eid


  • 2-s2.0-84925537030

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=4772&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/3753

Number Of Pages


  • 33

Start Page


  • 375

End Page


  • 408

Volume


  • 81

Issue


  • 3