On Levi subgroups and the Levi decomposition for groups definable in o-minimal structures

Annalisa Conversano, and Anand Pillay. "On Levi subgroups and the Levi decomposition for groups definable in o-minimal structures." Fundamenta Mathematicae 222.1 (2013): 49-62. <http://eudml.org/doc/282862>.

@article{AnnalisaConversano2013,
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 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.},
author = {Annalisa Conversano, Anand Pillay},
journal = {Fundamenta Mathematicae},
keywords = {Levi decomposition; ind-definable semisimple; o-minimality},
language = {eng},
number = {1},
pages = {49-62},
title = {On Levi subgroups and the Levi decomposition for groups definable in o-minimal structures},
url = {http://eudml.org/doc/282862},
volume = {222},
year = {2013},
}

TY - JOUR
AU - Annalisa Conversano
AU - Anand Pillay
TI - On Levi subgroups and the Levi decomposition for groups definable in o-minimal structures
JO - Fundamenta Mathematicae
PY - 2013
VL - 222
IS - 1
SP - 49
EP - 62
AB - 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.
LA - eng
KW - Levi decomposition; ind-definable semisimple; o-minimality
UR - http://eudml.org/doc/282862
ER -