Definability in the group of infinitesimals of a compact Lie group
Confluentes Mathematici, Volume 11 (2019) no. 2, pp. 3-23.

We show that for G a simple compact Lie group, the infinitesimal subgroup G 00 is bi-interpretable with a real closed convexly valued field. We deduce that for G an infinite definably compact group definable in an o-minimal expansion of a field, G 00 is bi-interpretable with the disjoint union of a (possibly trivial) -vector space and finitely many (possibly zero) real closed valued fields. We also describe the isomorphisms between such infinitesimal subgroups, and along the way prove that every definable field in a real closed convexly valued field R is definably isomorphic to R.

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DOI: 10.5802/cml.58
Classification: 03C64, 22E15
Keywords: Model Theory, Compact Lie Group, Infinitesimal Subgroup, O-Minimality, Bi-interpretation, Valued Field
Bays, Martin 1; Peterzil, Ya’acov 2

1 Institut für Logik und Grundlagenforschung, Fachbereich Mathematik und Informatik, Universität Münster, Einsteinstrasse 62, 48149 Münster, Germany
2 Department of Mathematics, University of Haifa, Haifa, Israel
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Bays, Martin; Peterzil, Ya’acov. Definability in the group of infinitesimals of a compact Lie group. Confluentes Mathematici, Volume 11 (2019) no. 2, pp. 3-23. doi : 10.5802/cml.58. http://www.numdam.org/articles/10.5802/cml.58/

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