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Simplicity of twisted C∗-algebras of higher-rank graphs and crossed products by quasifree actions

Journal Article


Abstract


  • We characterise simplicity of twisted C∗-algebras of row-finite κ-graphs with no sources. We show that each 2-cocycle on a cofinal κ-graph determines a canonical secondcohomology class for the periodicity group of the graph. The groupoid of the κ-graph then acts on the cartesian product of the infinite-path space of the graph with the dual group of the centre of any bicharacter representing this second-cohomology class. The twisted κ-graph algebra is simple if and only if this action is minimal. We apply this result to characterise simplicity for many twisted crossed products of κ-graph algebras by quasifree actions of free abelian groups.

Publication Date


  • 2016

Citation


  • Kumjian, A., Pask, D. & Sims, A. (2016). Simplicity of twisted C∗-algebras of higher-rank graphs and crossed products by quasifree actions. Journal of Noncommutative Geometry, 10 (2), 515-549.

Scopus Eid


  • 2-s2.0-84976510438

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/5732

Number Of Pages


  • 34

Start Page


  • 515

End Page


  • 549

Volume


  • 10

Issue


  • 2

Abstract


  • We characterise simplicity of twisted C∗-algebras of row-finite κ-graphs with no sources. We show that each 2-cocycle on a cofinal κ-graph determines a canonical secondcohomology class for the periodicity group of the graph. The groupoid of the κ-graph then acts on the cartesian product of the infinite-path space of the graph with the dual group of the centre of any bicharacter representing this second-cohomology class. The twisted κ-graph algebra is simple if and only if this action is minimal. We apply this result to characterise simplicity for many twisted crossed products of κ-graph algebras by quasifree actions of free abelian groups.

Publication Date


  • 2016

Citation


  • Kumjian, A., Pask, D. & Sims, A. (2016). Simplicity of twisted C∗-algebras of higher-rank graphs and crossed products by quasifree actions. Journal of Noncommutative Geometry, 10 (2), 515-549.

Scopus Eid


  • 2-s2.0-84976510438

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/5732

Number Of Pages


  • 34

Start Page


  • 515

End Page


  • 549

Volume


  • 10

Issue


  • 2