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Preprint Number 998

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998. Frécon Olivier
Linearity of groups definable in o-minimal structures
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Submission date: 28 January 2016

Abstract:

We consider an arbitrary o-minimal structure M and a definably connected definable group G.
The main theorem provides definable real closed fields R_1,...,R_k such that G/Z(G) is definably isomorphic to a direct product of definable subgroups of GL(n_1,_R1),...,GL(n_k,R_k), where Z(G) denotes the center of G.
It follows from this result a Levi decomposition for G, and that [G,G]Z(G)/Z(G) is definable and definably isomorphic to a direct product of semialgebraic linear groups over R_1,...,R_k.

Mathematics Subject Classification: 03C64

Keywords and phrases: o-minimal structure, semialgebraic group, Levi decomposition

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