Gauge Invariant Uniqueness Theorem for Corners of k-graphs

2005/06/29 by Stephen Allen, Allen, Stephen
Mathematics · #46L05 #Advanced Operator Algebra Research #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #Point processes and geometric inequalities #math.OA #msc:46L05

paper · pdf · doi:10.48550/arxiv.math/0506582

12 pages, no figures

arxiv created 2005/06/29 · openalex publication_date 2005/06/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a finitely aligned k-graph Λ with X a set of vertices in Λ we define a universal C*-algebra called C^*(Λ,X) generated by partial isometries. We show that C^*(Λ,X) is isomorphic to the corner P_XC^*(Λ)P_X, where P_X is the sum of vertex projections in X. We then prove a version of the Gauge Invariant Uniqueness Theorem for C^*(Λ,X), and then use the theorem to prove various results involving fullness, simplicity and Morita equivalence as well as new results involving symbolic dynamics.

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