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arXiv · 1407.6427

Crossed products and twisted $k$-graph algebras

Nathan Brownlowe·Valentin Deaconu·Alex Kumjian·David Pask
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Abstract

An automorphism $β$ of a $k$-graph $Λ$ induces a crossed product $C^* ( Λ) \rtimes_β\mathbb{Z}$ which is isomorphic to a $(k+1)$-graph algebra $C^* ( Λ\times_β\mathbb{Z})$. 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

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Nathan Brownlowe, Valentin Deaconu, Alex Kumjian, David Pask. 2014-07-24. Crossed products and twisted $k$-graph algebras. https://arxiv.org/abs/1407.6427

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