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

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Conversano A., Pillay A.

Fundamenta Mathematicae

2013

tom 222

nr 1

49-62

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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Conversano A.

1 Pillay A.

1 2013

Wyniki wyszukiwania

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