Definability in the group of infinitesimals of a compact Lie group
Confluentes Mathematici, Tome 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.

Reçu le : 2019-02-04
Révisé le : 2019-07-22
Accepté le : 2019-08-06
Publié le : 2020-03-09
DOI : https://doi.org/10.5802/cml.58
Classification : 03C64,  22E15
Mots clés: Model Theory, Compact Lie Group, Infinitesimal Subgroup, O-Minimality, Bi-interpretation, Valued Field
@article{CML_2019__11_2_3_0,
     author = {Martin Bays and Ya'acov Peterzil},
     title = {Definability in the group of infinitesimals of a compact Lie group},
     journal = {Confluentes Mathematici},
     publisher = {Institut Camille Jordan},
     volume = {11},
     number = {2},
     year = {2019},
     pages = {3-23},
     doi = {10.5802/cml.58},
     language = {en},
     url = {cml.centre-mersenne.org/item/CML_2019__11_2_3_0/}
}
Martin Bays; Ya’acov Peterzil. Definability in the group of infinitesimals of a compact Lie group. Confluentes Mathematici, Tome 11 (2019) no. 2, pp. 3-23. doi : 10.5802/cml.58. https://cml.centre-mersenne.org/item/CML_2019__11_2_3_0/

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