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Preprint Number 1669

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1669. Alf Onshuus and Sacha Post
A definability criterion for linear Lie groups
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Submission date: 24 October 2019

Abstract:

It is known since [7] that any group definable in an o-minimal expansion of the real field can be equipped with a Lie group structure. It is then natural to ask when does a Lie group is Lie isomorphic to a group definable in such expansion. Conversano, Starchenko and the first author answered this question in [2] in the case where the group is solvable. We give here a criterion in the case where the group is linear. More precisely if G is a linear Lie group it is isomorphic to a group definable in an o-minimal expansion of the reals if and only if its solvable radical is isomorphic to such group.

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Full text arXiv 1910.11287: pdf, ps.


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