Examples of *-commuting maps

Details Examples of *-commuting maps Examples of *-commuting maps

2011-01-19

arxiv.org/abs/1101.3795v1

Mathematics

Operator Algebras

Scientific paper

We introduce the concept of a $1$-coaligned $k$-graph and prove that the shift maps of a $k$-graph pairwise $*$-commute if and only if the $k$-graph is $1$-coaligned. We then prove that for $2$-graphs $\Lambda$ generated from basic data $*$-commuting shift maps is equivalent to a condition that implies that $C^*(\Lambda)$ is simple and purely infinite. We then consider full shift spaces and introduce a condition on a block map which ensures the associated sliding block code $*$-commutes with the shift.

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