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Gauge-Invariant Ideals in the C*-Algebras of Finitely Aligned Higher-Rank Graphs

Published online by Cambridge University Press:  20 November 2018

Aidan Sims
Aidan Sims*
Affiliation:
School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Australia e-mail: Aidan.Sims@newcastle.edu.au
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Abstract

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We produce a complete description of the lattice of gauge-invariant ideals in ${{C}^{*}}(\Lambda )$ for a finitely aligned $k$-graph $\Lambda $. We provide a condition on $\Lambda $ under which every ideal is gauge-invariant. We give conditions on $\Lambda $ under which ${{C}^{*}}(\Lambda )$ satisfies the hypotheses of the Kirchberg–Phillips classification theorem.

Keywords

46L05Graphs as categoriesgraph algebraC*-algebra
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 58 , Issue 6 , 01 December 2006 , pp. 1268 - 1290
Copyright
Copyright © Canadian Mathematical Society 2006

References

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