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arXiv · 1311.2873

A note on real algebraic groups

Hassan Azad·Indranil Biswas
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Abstract

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.

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Hassan Azad, Indranil Biswas. 2013-11-12. A note on real algebraic groups. https://arxiv.org/abs/1311.2873

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