Definability in the group of infinitesimals of a compact lie group

Martin Bays, Ya’Acov Peterzil

Research output: Contribution to journalArticlepeer-review


We show that for G a simple compact Lie group, the infinitesimal subgroup G00 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, G00 is bi-interpretable with the disjoint union of a (possibly trivial) Q-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.

Original languageEnglish
Pages (from-to)3-23
Number of pages21
JournalConfluentes Mathematici
Issue number2
StatePublished - 2019

Bibliographical note

Publisher Copyright:
© 2019, Institut Camille Jordan. All rights reserved.


  • Bi-interpretation
  • Compact Lie Group
  • Infinitesimal Subgroup
  • Model Theory
  • O-Minimality
  • Valued Field

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Mathematical Physics
  • Applied Mathematics


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