arXiv subjects

Julian Gonzales

Publications and source records attributed to Julian Gonzales.

3 recordsLinked to original sources

arXiv2026

On dense subalgebras of the singular ideal in groupoid C*-algebras

We prove that ideals in amenable second-countable non-Hausdorff étale groupoid $C^*$-algebras are determined by their isotropy fibres. As an application, we characterise when the singular functions in Connes' algebra are dense in the singular ideal in terms of a property of explicit ideals in the isotropy group $C^*$-algebras. We then show this density property holds for all $C^*$-algebras of groupoids with finite-by-nilpotent isotropy groups.

math.OA↗

arXiv2026

Graph C*-algebras are singly generated

We show that the $C^*$-algebra of a countable directed graph is singly generated. As a consequence, any $C^*$-algebra generated by a countable family of projections and partial isometries satisfying Cuntz-Krieger relations is singly generated.

math.OA↗

arXiv2025

On Hausdorff covers for non-Hausdorff groupoids

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 when singular ideals vanish in Steinberg algebras over arbitrary rings. We also completely characterise when $C^*$-algebraic singular ideals have trivial intersection with the non-Hausdorff analogue of subalgebras of continuous, compactly supported functions. This leads to a characterisation when $C^*$-algebraic singular ideals vanish for groupoids satisfying a finiteness condition. Moreover, our approach leads to further sufficient vanishing criteria for singular ideals and reduces questions about simplicity, the ideal intersection property, amenability and nuclearity for non-Hausdorff étale groupoids to the Hausdorff case.

math.OA↗