Gauge-invariant ideals in the C*-algebras of finitely aligned higher-rank graphs

2004/06/29 by Aidan Sims, Sims, Aidan · 4 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Noncommutative and Quantum Gravity Theories #math.OA #msc:46L05

paper · pdf · doi:10.48550/arxiv.math/0406592

19 pages. Additional references added in Section 8. Title of Section 6 changed from "The lattice structure" to "The lattice order"

arxiv created 2004/08/16 · arxiv updated 2009/12/01

Abstract

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

Cited by

• Groupoids of finitely aligned higher-rank graphs via filters and graph morphisms
• Relating insplittings of 2-graphs and of textile systems
• Topological spaces associated to higher-rank graphs
• Graded Steinberg algebras and their representations

Related

• The ideal structure of the C*-algebras of infinite graphs
• ℕ-Graph C^*-Algebras
• The C^*-algebras of finitely aligned higher-rank graphs
• A class of C^*-algebras generalizing both graph algebras and homeomorphism C^*-algebras III, ideal structures
• Ideals in Graph Algebras