Realising the C*-algebra of a higher-rank graph as an Exel crossed product
Abstract
We use the boundary-path space of a finitely-aligned k-graph to construct a compactly-aligned product system X, and we show that the graph algebra C*() is isomorphic to the Cuntz-Nica-Pimsner algebra NO(X). In this setting, we introduce the notion of a crossed product by a semigroup of partial endomorphisms and partially-defined transfer operators by defining it to be NO(X). We then compare this crossed product with other definitions in the literature.
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