  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.
