arXiv subjects

Paulette N. Willis

Publications and source records attributed to Paulette N. Willis.

3 recordsLinked to original sources

arXiv2012

Examples of *-commuting maps

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 $Λ$ generated from basic data *-commuting shift maps is equivalent to a condition that implies that $C^*(Λ)$ 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.

math.OA↗

arXiv2011

The crossed-product structure of C*-algebras arising from topological dynamical systems

We show that every topological k-graph constructed from a locally compact Hausdorff space Ω and a family of pairwise commuting local homeomorphisms on Ω satisfying a uniform boundedness condition on the cardinalities of inverse images may be realized as a semigroup crossed product in the sense of Larsen.

math.OA↗

arXiv2010

Local homeomorphisms that *-commute with the shift

Exel and Renault proved that a sliding block code on a one-sided shift space coming from a progressive block map is a local homeomorphism. We provide a counterexample showing that the converse does not hold. We use this example to generalize the notion of progressive to a property of block maps we call weakly progressive, and we prove that a sliding block code coming from a weakly progressive block map is a local homeomorphism. We also introduce the notion of a regressive block map and prove that a sliding block code *-commutes with the shift map if and only if it comes from a regressive block map. We also prove that a sliding block code is a local homeomorphism and *-commutes with the shift map if and only if it is a k-fold covering map defined from a regressive block map.

math.OA↗