The C∗-algebras of finitely aligned higher-rank graphs
Copyright policy )The C∗-algebras of finitely aligned higher-rank graphs
We generalise the theory of Cuntz-Krieger families and graph algebras to the class of finitely aligned $k$-graphs. This class contains in particular all row-finite $k$-graphs. The Cuntz-Krieger relations for non-row-finite $k$-graphs look significantly different from the usual ones, and this substantially complicates the analysis of the graph algebra. We prove a gauge-invariant uniqueness theorem and a Cuntz-Krieger uniqueness theorem for the $C^*$-algebras of finitely aligned $k$-graphs.
27 pages
- University of Newcastle Australia Australia
Cuntz--Krieger algebra, Graph algebra, 46L05, Mathematics - Operator Algebras, uniqueness, Cuntz–Krieger algebra, General theory of \(C^*\)-algebras, Cuntz–Krieger families, FOS: Mathematics, Uniqueness, Operator Algebras (math.OA), graph algebra, Analysis
Cuntz--Krieger algebra, Graph algebra, 46L05, Mathematics - Operator Algebras, uniqueness, Cuntz–Krieger algebra, General theory of \(C^*\)-algebras, Cuntz–Krieger families, FOS: Mathematics, Uniqueness, Operator Algebras (math.OA), graph algebra, Analysis
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