Realising the C*-algebra of a higher-rank graph as an Exel crossed product

Details Realising the C*-algebra of a higher-rank graph as an Exel crossed product Realising the C*-algebra of a higher-rank graph as an Exel crossed product

2009-12-23

arxiv.org/abs/0912.4635v2

Mathematics

Operator Algebras

Corrections made to Section 5.3

Scientific paper

We use the boundary-path space of a finitely-aligned k-graph \Lambda to construct a compactly-aligned product system X, and we show that the graph algebra C^*(\Lambda) 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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