7 papers
On dense subalgebras of the singular ideal in groupoid C*-algebras
Julian Gonzales, Jeremy B. Hume
We prove that ideals in amenable second-countable non-Hausdorff étale groupoid -algebras are determined by their isotropy fibres. As an application, we characterise when the s…
Characterizations of zero singular ideal in étale groupoid C*-algebras via compressible maps
Jeremy B. Hume
We show the singular ideal in a non-Hausdorff étale groupoid C*-algebra is zero if and only if every unit is contained, at the level of group representation theory, in the collecti…
On Hausdorff covers for non-Hausdorff groupoids
Kevin Aguyar Brix, Julian Gonzales, Jeremy B. Hume +1
We develop a new approach to non-Hausdorff étale groupoids and their algebras based on Timmermann's construction of Hausdorff covers. As an application, we completely characterise…
Minimal covers with continuity-preserving transfer operators for topological dynamical systems
Kevin Aguyar Brix, Jeremy B. Hume, Xin Li
Given a non-invertible dynamical system with a transfer operator, we show there is a minimal cover with a transfer operator that preserves continuous functions. We also introduce a…
Katsura-Exel-Pardo self-similar actions, Putnam's binary factors and their limit spaces
Jeremy B. Hume, Michael F. Whittaker
We show that the dynamical system associated by Putnam to a pair of graph embeddings is identical to the shift map on the limit space of a self-similar groupoid action on a graph.…
The K-theory of the C*-algebras associated to rational functions
Jeremy B. Hume
We compute the K-theory of the three C*-algebras associated to a rational function R acting on the Riemann sphere, its Fatou set, and its Julia set. The latter C*-algebra is a unit…
KK-duality for self-similar groupoid actions on graphs
Nathan Brownlowe, Alcides Buss, Daniel Gonçalves +3
We extend Nekrashevych's -duality for -algebras of regular, recurrent, contracting self-similar group actions to regular, contracting self-similar groupoid actions on a gr…