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 a rather strong definition of ind-definable semisimple subgroup, we prove that G has a unique maximal ind-definable semisimple subgroup S, up to conjugacy, and that G = R· S 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm222-1-3,
author = {Annalisa Conversano and Anand Pillay},
title = {On Levi subgroups and the Levi decomposition for groups definable in o-minimal structures},
journal = {Fundamenta Mathematicae},
volume = {220},
year = {2013},
pages = {49-62},
zbl = {1285.03037},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm222-1-3}
}
Annalisa Conversano; Anand Pillay. On Levi subgroups and the Levi decomposition for groups definable in o-minimal structures. Fundamenta Mathematicae, Tome 220 (2013) pp. 49-62. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm222-1-3/