Geodesic
On Levi subgroups and the Levi decomposition for groups definable in $o$-minimal structures
Annalisa Conversano 1   ; Anand Pillay 2
1 Institute of Natural and Mathematical Sciences Massey University P/bag 102-904 NSMC Auckland, NZ
2 Department of Pure Mathematics University of Leeds LS2 9JT Leeds, UK
Fundamenta Mathematicae, Tome 222 (2013) no. 1, pp. 49-62 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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 $G = R\cdot S$ 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 $G$.
DOI : 10.4064/fm222-1-3
Keywords: study analogues notions lie theory levi subgroup levi decomposition groups definable o minimal expansion real closed field rather strong definition ind definable semisimple subgroup prove has unique maximal ind definable semisimple subgroup conjugacy cdot where solvable radical prove semisimple subalgebra lie algebra corresponds unique ind definable semisimple subgroup

Annalisa Conversano  1   ; Anand Pillay  2

1 Institute of Natural and Mathematical Sciences Massey University P/bag 102-904 NSMC Auckland, NZ
2 Department of Pure Mathematics University of Leeds LS2 9JT Leeds, UK 
@article{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},
     pages = {49--62},
     year = {2013},
     volume = {222},
     number = {1},
     doi = {10.4064/fm222-1-3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm222-1-3/}
}
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
SP  - 49
EP  - 62
VL  - 222
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm222-1-3/
DO  - 10.4064/fm222-1-3
LA  - en
ID  - 10_4064_fm222_1_3
ER  - 
%0 Journal Article
%A Annalisa Conversano
%A Anand Pillay
%T On Levi subgroups and the Levi decomposition for
 groups definable in $o$-minimal structures
%J Fundamenta Mathematicae
%D 2013
%P 49-62
%V 222
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/fm222-1-3/
%R 10.4064/fm222-1-3
%G en
%F 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 222 (2013) no. 1, pp. 49-62. doi: 10.4064/fm222-1-3

Cité par Sources :