Consider a projective limit G of finite groups Gn. Fix a compatible family n of coactions of the Gn on a C*-algebra A. From this data we obtain a coaction of G on A. We show that the coaction crossed product of A by is isomorphic to a direct limit of the coaction crossed products of A by the n. If A=C*() for some k-graph , and if the coactions n correspond to skew-products of , then we can say more. We prove that the coaction crossed product of C*() by may be realized as a full corner of the C*-algebra of a (k+1)-graph. We then explore connections with Yeends topological higher-rank graphs and their C*-algebras.
- Graph algebra
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