On Levi subgroups and the Levi decomposition for groups definable in o-minimal structures
Logic
2011-11-11 v1 Group Theory
Abstract
We study analogues of the notions from Lie theory of Levi subgroup and Levi decomposition, in the case of groups G definable in an o-minimal expansion of a real closed field. With suitable definitions, we prove that G has a unique maximal ind-definable semisimple subgroup S, up to conjugacy, and that G = RS where R is the solvable radical of G. We also prove that any semisimple subalgebra of the Lie algebra of G corresponds to a unique ind-definable semisimple subgroup of G.
Cite
@article{arxiv.1111.2369,
title = {On Levi subgroups and the Levi decomposition for groups definable in o-minimal structures},
author = {Annalisa Conversano and Anand Pillay},
journal= {arXiv preprint arXiv:1111.2369},
year = {2011}
}
Comments
16 pages