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Preprint Number 1669
1669. Alf Onshuus and Sacha Post A definability criterion for linear Lie groups E-mail: 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. Mathematics Subject Classification: Keywords and phrases: |

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