Real points in a homogeneous space of a real algebraic group

Abstract

Let G be a linear algebraic group over the field of real numbers R, and let Y be a right homogeneous space of G. We wish to find a real point of Y or to prove that Y has no real points. We describe a method to do that, implicitly using second nonabelian Galois cohomology. Our method is suitable for computer-assisted calculations.

V1: 18 pages, V2: 22 pages. An appendix added

References in corpus (1)

• Real graded Lie algebras, Galois cohomology, and classification of trivectors in R^9