\begin{thebibliography}{PPS00b}

\bibitem[Ber07]{B-spectra}
Alessandro Berarducci.
\newblock o-minimal spectra, infinitesimal subgroups and cohomology.
\newblock {\em J. Symbolic Logic}, 72(4):1177--1193, 2007.

\bibitem[Bou89]{Bourbaki-Lie}
Nicolas Bourbaki.
\newblock {\em Lie groups and {L}ie algebras. {C}hapters 1--3}.
\newblock Elements of Mathematics (Berlin). Springer-Verlag, Berlin, 1989.
\newblock Translated from the French, Reprint of the 1975 edition.

\bibitem[Car30]{cartan}
Elie Cartan.
\newblock Sur les repr\'{e}sentations lin\'{e}aires des groupes clos.
\newblock {\em Comment. Math. Helv.}, 2(1):269--283, 1930.

\bibitem[CD83]{cherlinDickmann}
Gregory Cherlin and Max~A. Dickmann.
\newblock Real closed rings. {II}. {M}odel theory.
\newblock {\em Ann. Pure Appl. Logic}, 25(3):213--231, 1983.

\bibitem[DM16]{dAndreaMaffei}
Alessandro D'Andrea and Andrea Maffei.
\newblock Commutators of small elements in compact semisimple groups and {L}ie
  algebras.
\newblock {\em J. Lie Theory}, 26(3):683--690, 2016.

\bibitem[vdD98]{vdD-omin}
L.~van~den Dries.
\newblock {\em Tame topology and o-minimal structures}, volume 248 of {\em
  London Mathematical Society Lecture Note Series}.
\newblock Cambridge University Press, Cambridge, 1998.

\bibitem[FH91]{FultonHarris}
William Fulton and Joe Harris.
\newblock {\em Representation theory}, volume 129 of {\em Graduate Texts in
  Mathematics}.
\newblock Springer-Verlag, New York, 1991.
\newblock A first course, Readings in Mathematics.

\bibitem[HPP11]{HPP-central}
Ehud Hrushovski, Ya'acov Peterzil, and Anand Pillay.
\newblock On central extensions and definably compact groups in o-minimal
  structures.
\newblock {\em J. Algebra}, 327:71--106, 2011.

\bibitem[HR18]{HR-metastable}
Ehud Hrushovski and Silvain Rideau.
\newblock Valued fields, metastable groups.
\newblock 2018.
\newblock arXiv:1709.08801v3 [math.LO].

\bibitem[Kna02]{Knapp}
Anthony~W. Knapp.
\newblock {\em Lie groups beyond an introduction}, volume 140 of {\em Progress
  in Mathematics}.
\newblock Birkh\"auser Boston, Inc., Boston, MA, second edition, 2002.

\bibitem[MMS00]{MMS-weakOMin}
Dugald Macpherson, David Marker, and Charles Steinhorn.
\newblock Weakly o-minimal structures and real closed fields.
\newblock {\em Trans. Amer. Math. Soc.}, 352(12):5435--5483, 2000.

\bibitem[Ma{\v{r}}07]{Marikova}
Jana Ma{\v{r}}\'{i}kov\'{a}.
\newblock Type-definable and invariant groups in o-minimal structures.
\newblock {\em J. Symbolic Logic}, 72(1):67--80, 2007.

\bibitem[Mel06]{Mellor-RCVFEI}
T.~Mellor.
\newblock Imaginaries in real closed valued fields.
\newblock {\em Ann. Pure Appl. Logic}, 139(1-3):230--279, 2006.

\bibitem[NP91]{NP-compactLie}
Ali Nesin and Anand Pillay.
\newblock Some model theory of compact {L}ie groups.
\newblock {\em Trans. Amer. Math. Soc.}, 326(1):453--463, 1991.

\bibitem[OV90]{OV}
A.~L. Onishchik and \`E.~B. Vinberg.
\newblock {\em Lie groups and algebraic groups}.
\newblock Springer Series in Soviet Mathematics. Springer-Verlag, Berlin, 1990.
\newblock Translated from the Russian and with a preface by D. A. Leites.

\bibitem[OPP96]{OPP-groupsRings}
Margarita Otero, Ya'acov Peterzil, and Anand Pillay.
\newblock On groups and rings definable in o-minimal expansions of real closed
  fields.
\newblock {\em Bull. London Math. Soc.}, 28(1):7--14, 1996.

\bibitem[PPS00a]{PPS-defblySimple}
Y.~Peterzil, A.~Pillay, and S.~Starchenko.
\newblock Definably simple groups in o-minimal structures.
\newblock {\em Trans. Amer. Math. Soc.}, 352(10):4397--4419, 2000.

\bibitem[PPS00b]{PPS-simpleAlgGrpsRCF}
Ya'acov Peterzil, Anand Pillay, and Sergei Starchenko.
\newblock Simple algebraic and semialgebraic groups over real closed fields.
\newblock {\em Trans. Amer. Math. Soc.}, 352(10):4421--4450, 2000.

\bibitem[PS98]{PS-trichotomy}
Ya'acov Peterzil and Sergei Starchenko.
\newblock A trichotomy theorem for o-minimal structures.
\newblock {\em Proc. London Math. Soc. (3)}, 77(3):481--523, 1998.

\bibitem[PS99]{PS-defbleCompactness}
Ya'acov Peterzil and Charles Steinhorn.
\newblock Definable compactness and definable subgroups of o-minimal groups.
\newblock {\em J. London Math. Soc. (2)}, 59(3):769--786, 1999.

\bibitem[Pil88]{P-groupsFieldsOMin}
Anand Pillay.
\newblock On groups and fields definable in {$o$}-minimal structures.
\newblock {\em J. Pure Appl. Algebra}, 53(3):239--255, 1988.

\bibitem[Pil89]{pillay-fieldsQp}
Anand Pillay.
\newblock On fields definable in {${\bf Q}_p$}.
\newblock {\em Arch. Math. Logic}, 29(1):1--7, 1989.

\bibitem[Pil04]{Pillay-conjecture}
Anand Pillay.
\newblock Type-definability, compact {L}ie groups, and o-minimality.
\newblock {\em J. Math. Log.}, 4(2):147--162, 2004.

\bibitem[Poi88]{poizat-BT}
Bruno Poizat.
\newblock M{M}. {B}orel, {T}its, {Z}il{'}ber et le {G}\'{e}n\'{e}ral
  {N}onsense.
\newblock {\em J. Symbolic Logic}, 53(1):124--131, 1988.

\bibitem[vdW33]{waerden}
B.~L. van~der Waerden.
\newblock Stetigkeitss\"{a}tze f\"{u}r halbeinfache {L}iesche {G}ruppen.
\newblock {\em Math. Z.}, 36(1):780--786, 1933.

\bibitem[Woi17]{woit}
Peter Woit.
\newblock {\em Quantum theory, groups and representations}.
\newblock Springer, Cham, 2017.

\end{thebibliography}
