Crossed products and twisted $k$-graph algebras

Abstract

An automorphism $\beta$ of a $k$-graph $\Lambda$ induces a crossed product $C^{\ast }(\Lambda ){⋊}_{\beta }\mathbb{Z}$ which is isomorphic to a $(k+1)$-graph algebra $C^{\ast }(\Lambda {\times }_{\beta }\mathbb{Z})$. In this paper we show how this process interacts with $k$-graph $C^{\ast }$-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

15 pages, 2 figures

References in corpus (3)

• Simplicity of C*-algebras associated to higher-rank graphs
• Crossed products of k-graph C*-algebras by Z^l
• Fundamental groupoids of k-graphs