Abstract
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 language | American English |
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Pages (from-to) | 3-23 |
Number of pages | 21 |
Journal | Confluentes Mathematici |
Volume | 11 |
Issue number | 2 |
DOIs | |
State | Published - 2019 |
Keywords
- Bi-interpretation
- Compact Lie Group
- Infinitesimal Subgroup
- Model Theory
- O-Minimality
- Valued Field
All Science Journal Classification (ASJC) codes
- Applied Mathematics
- Mathematics (miscellaneous)
- Mathematical Physics