Cartan subgroups and regular points of o-minimal groups
Logic
2019-04-24 v1
Abstract
Let G be a group definable in an o-minimal structure M. We prove that the union of the Cartan subgroups of G is a dense subset of G. When M is an expansion of a real closed field we give a characterization of Cartan subgroups of G via their Lie algebras which allow us to prove firstly, that every Cartan subalgebra of the Lie algebra of G is the Lie algebra of a definable subgroup - a Cartan subgroup of G -, and secondly, that the set of regular points of G - a dense subset of G - is formed by points which belong to a unique Cartan subgroup of G.
Keywords
Cite
@article{arxiv.1707.02738,
title = {Cartan subgroups and regular points of o-minimal groups},
author = {Elias Baro and Alessandro Berarducci and Margarita Otero},
journal= {arXiv preprint arXiv:1707.02738},
year = {2019}
}