Finite nuclear dimension of crossed products by p-adic numbers (Master disputation)

28.04.2025, 14:15  –  Haus 9, Raum 1.10
Forschungsseminar: Gruppen und Operatoralgebren

Dominik Ulrich

In this presentation we will look at crossed products of the form \(C_0(X)\rtimes_\alpha \mathbb Q_p\), where \(X\) is a locally compact, second-countable Hausdorff space and \( \alpha: \mathbb Q_p\to \text{Aut}(C_0(X))\) is induced by a continuous action of the p-adic numbers \(\mathbb Q_p\) on \(X\) and investigate if it is possible to bound its nuclear dimension in terms of the covering dimension of \(X\). To that end I will introduce crossed products, the p-adic numbers and the nuclear dimension of \(C^*\)-algebras before presenting a strategy to tackle the aforementioned problem.