New York Journal of Mathematics
Volume 22 (2016) 229-250

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Nathan Brownlowe, Valentin Deaconu, Alex Kumjian, and David Pask

Crossed products and twisted k-graph algebras

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Published: March 7, 2016
Keywords: Higher-rank graph; C*-algebra; cohomology; crossed product.
Subject: Primary 46L05; Secondary 18G60, 55N10.
Abstract
An automorphism β of a k-graph Λ induces a crossed product C*(Λ)\rtimesβZ which is isomorphic to a (k+1)-graph algebra C*(Λ×βZ). In this paper we show how this process interacts with k-graph C*-algebras which have been twisted by an element of their second cohomology group. This analysis is done using a long exact sequence in cohomology associated to this data. We conclude with some examples.

Acknowledgements

This research was supported by the Australian Research Council and the University of Wollongong Research Committee.
Author information

Nathan Brownlowe:
School of Mathematics and Applied Statistics, The University of Wollongong, NSW 2522, AUSTRALIA
nathanb@uow.edu.au

Valentin Deaconu:
Department of Mathematics (084), University of Nevada, Reno NV 89557-0084, USA
vdeaconu@unr.edu

Alex Kumjian:
Department of Mathematics (084), University of Nevada, Reno NV 89557-0084, USA
alex@unr.edu

David Pask:
School of Mathematics and Applied Statistics, The University of Wollongong, NSW 2522, AUSTRALIA
dpask@uow.edu.au