2013/11/12 by Hassan Azad, Indranil Biswas, Azad, Hassan +1
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR
paper · pdf · doi:10.48550/arxiv.1311.2873
7 pages, no figure
arxiv created 2013/11/12 · arxiv updated 2013/11/13
The efficacy of using complexifications to understand the structure of real algebraic groups is demonstrated. In particular the following results are proved: a) If L is an algebraic subgroup of a connected real algebraic group G such that the complexification of L contains a maximal torus of the complexification of G, then L contains a Cartan subgroup of G b) Let G be a solvable real algebraic group whose eigenvalues are all real. If the complexification of G operates algebraically on a complex variety V, and some G orbit is compact, then this orbit is a point.