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Realising the c*-algebra of a higher-rank graph as an exel's crossed product

Journal Article


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Abstract


  • 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.

UOW Authors


  •   Brownlowe, Nathan (external author)

Publication Date


  • 2012

Citation


  • Brownlowe, N. (2012). Realising the c*-algebra of a higher-rank graph as an exel's crossed product. Journal of Operator Theory, 68 (1), 101-130.

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1256&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/251

Number Of Pages


  • 29

Start Page


  • 101

End Page


  • 130

Volume


  • 68

Issue


  • 1

Abstract


  • 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.

UOW Authors


  •   Brownlowe, Nathan (external author)

Publication Date


  • 2012

Citation


  • Brownlowe, N. (2012). Realising the c*-algebra of a higher-rank graph as an exel's crossed product. Journal of Operator Theory, 68 (1), 101-130.

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1256&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/251

Number Of Pages


  • 29

Start Page


  • 101

End Page


  • 130

Volume


  • 68

Issue


  • 1