Linear Groups Definable in o-Minimal Structures☆

By Ya'acov Peterzil, Anand Pillay, Sergei Starchenko. 2002

58 citations recorded by the source corpus.

We study subgroups G of GL(n, R) definable in o-minimal expansions M = (R, +, · ,…) of a real closed field R. We prove several results such as: (a) G can be defined using just the field structure on R together with, if necessary, power functions, or an exponential function definable in M. (b) If G has no infinite, normal, definable abelian subgroup, then G is semialgebraic. We also characterize the definably simple groups definable in o-minimal structures as those groups elementarily equivalent to simple Lie groups, and we give a proof of the Kneser–Tits conjecture for real closed fields.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a2bdf197de0b71f54a1b11b87939b29988f25bf6

Citations in the corpus

• Groups, measures, and the NIP (2006, unknown): “If G is “semisimple”, namely has no proper connected infinite definable normal commutative subgroup, then by [17], G is an almost direct product of finitely many almost definably simple groups G1, .., Gk. (“Almost definably simple” means that the group is noncommutative and the quotient by some fini”