Galois cohomology of real semisimple groups via Kac labelings

Abstract

For a connected semisimple group G over the field of real numbers R, using a method of Onishchik and Vinberg, we compute the first Galois cohomology set H^1(R,G) in terms of Kac labelings of the affine Dynkin diagram of G.

This preprint supersedes arXiv:1506.06252. V.1, 35 pages. V.2, 36 pages, final version to appear in Transformation Groups