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On the K-theory of twisted higher-rank-graph C*-algebras

Journal Article


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Abstract


  • We investigate the K-theory of twisted higher-rank-graph algebras by adapting parts of Elliott’s computation of the K-theory of the rotation algebras. We show that each 2-cocycle on a higher-rank graph taking values in an abelian group determines a continuous bundle of twisted higher-rank graph algebras over the dual group. We use this to show that for a circle-valued 2-cocycle on a higher-rank graph obtained by exponentiating a real-valued cocycle, the K-theory of the twisted higher-rank graph algebra coincides with that of the untwisted one.

Publication Date


  • 2013

Citation


  • Kumjian, A., Pask, D. & Sims, A. (2013). On the K-theory of twisted higher-rank-graph C*-algebras. Journal of Mathematical Analysis and Applications, 401 (1), 104-113.

Scopus Eid


  • 2-s2.0-84872909103

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1498&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/493

Has Global Citation Frequency


Number Of Pages


  • 9

Start Page


  • 104

End Page


  • 113

Volume


  • 401

Issue


  • 1

Place Of Publication


  • United States

Abstract


  • We investigate the K-theory of twisted higher-rank-graph algebras by adapting parts of Elliott’s computation of the K-theory of the rotation algebras. We show that each 2-cocycle on a higher-rank graph taking values in an abelian group determines a continuous bundle of twisted higher-rank graph algebras over the dual group. We use this to show that for a circle-valued 2-cocycle on a higher-rank graph obtained by exponentiating a real-valued cocycle, the K-theory of the twisted higher-rank graph algebra coincides with that of the untwisted one.

Publication Date


  • 2013

Citation


  • Kumjian, A., Pask, D. & Sims, A. (2013). On the K-theory of twisted higher-rank-graph C*-algebras. Journal of Mathematical Analysis and Applications, 401 (1), 104-113.

Scopus Eid


  • 2-s2.0-84872909103

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1498&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/493

Has Global Citation Frequency


Number Of Pages


  • 9

Start Page


  • 104

End Page


  • 113

Volume


  • 401

Issue


  • 1

Place Of Publication


  • United States