Linearity of groups definable in o-minimal structures

• Olivier Frécon ^[1]
  1. [1] University of Poitiers

     University of Poitiers

     Arrondissement de Poitiers, Francia

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 2, 2017, págs. 1563-1598
• Idioma: inglés
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• Resumen

  • We consider an arbitrary o-minimal structureMand a definably connected definable group G. The main theorem provides definable real closed fields R1,...,Rk such that G/Z(G)is definably isomorphic to a direct product of definable subgroups of GLn1 (R1), . . . , GLnk (Rk ), where Z(G) denotes the center of G. From this, we derive a Levi decomposition for G and show that [G, G]Z(G)/Z(G)is definable and definably isomorphic to a direct product of semialgebraic linear groups over R1,...,Rk .