4 February 2026 — Padova

Borel subgroups of \(\mathsf{Aut}(\mathbb{A}^n)\)

Michael Chitayat, University of Padova

Abstract

Let \(X\) be an affine variety. It was recently proved that a connected solvable subgroup \(G \subseteq \mathsf{Aut}(X)\) can be decomposed as a semi-direct product \(G = T \ltimes U\) where \(T\) is an algebraic torus and \(U\) is a nested unipotent subgroup. A Borel subgroup of \(\mathsf{Aut}(X)\) is a maximal element of the set of connected solvable subgroups of \(\mathsf{Aut}(X)\). In this talk, I will discuss Borel subgroups of \(\mathsf{Aut}(X)\) with a focus on the special case where \(X = \mathbb{A}^n\). This is joint work with Andriy Regeta and Daniel Daigle.