2007/06/04 by David Pask, John Quigg, Pask, David +3
Mathematics · Physics and Astronomy · #46L05 (Primary) #46L55 (Secondary) #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.0706.0362
openalex publication_date 2007/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider a projective limit G of finite groups Gn. Fix a compatible family δn of coactions of the Gn on a C*-algebra A. From this data we obtain a coaction δof G on A. We show that the coaction crossed product of A by δis isomorphic to a direct limit of the coaction crossed products of A by the δn. If A = C*(Λ) for some k-graph Λ, and if the coactions δn correspond to skew-products of Λ, then we can say more. We prove that the coaction crossed-product of C*(Λ) by δmay be realised as a full corner of the C*-algebra of a (k+1)-graph. We then explore connections with Yeend's topological higher-rank graphs and their C*-algebras.