The Jordan property for Lie groups and automorphism groups of complex spaces

TL;DR

This paper proves that all connected n-dimensional real Lie groups are uniformly Jordan, leading to the conclusion that various algebraic and transformation groups over complex spaces and Riemannian manifolds are also Jordan.

Contribution

It establishes the uniform Jordan property for all connected n-dimensional real Lie groups, extending to algebraic groups over characteristic zero fields and certain transformation groups.

Findings

Connected n-dimensional real Lie groups are uniformly Jordan

Algebraic groups over characteristic zero fields are Jordan

Transformation groups of complex spaces and Riemannian manifolds are Jordan

Abstract

We prove that the family of all connected n-dimensional real Lie groups is uniformly Jordan for every n. This implies that all algebraic groups (not necessarily affine) over fields of characteristic zero and some transformation groups of complex spaces and Riemannian manifods are Jordan.