We show that for a simple compact Lie group, the infinitesimal subgroup is bi-interpretable with a real closed convexly valued field. We deduce that for an infinite definably compact group definable in an o-minimal expansion of a field, 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 is definably isomorphic to .
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Keywords: Model Theory, Compact Lie Group, Infinitesimal Subgroup, O-Minimality, Bi-interpretation, Valued Field
Martin Bays 1; Ya’acov Peterzil 2
@article{CML_2019__11_2_3_0, author = {Martin Bays and Ya{\textquoteright}acov Peterzil}, title = {Definability in the group of infinitesimals of a compact {Lie} group}, journal = {Confluentes Mathematici}, pages = {3--23}, publisher = {Institut Camille Jordan}, volume = {11}, number = {2}, year = {2019}, doi = {10.5802/cml.58}, language = {en}, url = {https://cml.centre-mersenne.org/articles/10.5802/cml.58/} }
TY - JOUR AU - Martin Bays AU - Ya’acov Peterzil TI - Definability in the group of infinitesimals of a compact Lie group JO - Confluentes Mathematici PY - 2019 SP - 3 EP - 23 VL - 11 IS - 2 PB - Institut Camille Jordan UR - https://cml.centre-mersenne.org/articles/10.5802/cml.58/ DO - 10.5802/cml.58 LA - en ID - CML_2019__11_2_3_0 ER -
%0 Journal Article %A Martin Bays %A Ya’acov Peterzil %T Definability in the group of infinitesimals of a compact Lie group %J Confluentes Mathematici %D 2019 %P 3-23 %V 11 %N 2 %I Institut Camille Jordan %U https://cml.centre-mersenne.org/articles/10.5802/cml.58/ %R 10.5802/cml.58 %G en %F CML_2019__11_2_3_0
Martin Bays; Ya’acov Peterzil. 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. https://cml.centre-mersenne.org/articles/10.5802/cml.58/
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