On Levi subgroups and the Levi decomposition for
groups definable in $o$-minimal structures
Fundamenta Mathematicae, Tome 222 (2013) no. 1, pp. 49-62
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 $G$.
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
Affiliations des auteurs :
Annalisa Conversano 1 ; Anand Pillay 2
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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},
publisher = {mathdoc},
volume = {222},
number = {1},
year = {2013},
doi = {10.4064/fm222-1-3},
language = {en},
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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
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