Real Algebraic and Analytic Geometry

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337. Annalisa Conversano, Anand Pillay:
On Levi subgroups and the Levi decomposition for groups definable in o-minimal structures.


Submission: 2011, December 2.

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. .

Mathematics Subject Classification (2010): 03C64, 22E15.

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