##### Sesión Lógica y Computabilidad

Diciembre 12, 16:10 ~ 16:50

## Commutators of simply-connected o-minimal groups

### Baro, Elías

Groups definable in an o-minimal expansion of a real closed field can be seen as a non-standard version of a Lie groupt (if the real closed field is the real field then such a group is actually a Lie group). For example, algebraic groups over a real closed field are o-minimal groups. In fact, at the kernel of the theory there is a finiteness phenomena that allow us to show that o-minimal and algebraic groups share some properties. In this sense, the commutator subgroup of an algebraic group is again algebraic. However, the commutator of a Lie group may not be a Lie subgroup (there are even solvable counterexamples). The commutator of an o-minimal group may not be definable; in \cite{cite1} we prove that it is so if the group is solvable. Commutators play an important role in any category of groups; \emph{e.g.} the latter result was used in \cite{cite2} to characterize which solvable Lie groups are definable in an o-minimal expansion of the real field. In this talk I will present these results and new insights concerning commutators of simply-connected o-minimal groups. \begin{thebibliography}{10} \bibitem{cite1} E. Baro, E. Jaligot, M. Otero, \emph{Commutators in groups definable in o-minimal structures}, Proc. Amer. Math. Soc. 140 (2012), no. 10, 3629--3643. \bibitem{cite2} A. Conversano, A. Onshuus, and S. Starchenko, \emph{Solvable Lie groups definable in o-minimal theories}, J. Inst. Math. Jussieu, to appear. \end{thebibliography}

Autores: Baro, Elías.