Galois cohomology and component group of a real reductive group
Group Theory
2024-10-04 v3 Algebraic Geometry
Number Theory
Representation Theory
Abstract
Let G be a connected reductive group over the field of real numbers R. Using results of our previous joint paper, we compute combinatorially the first Galois cohomology set H^1(R,G) in terms of reductive Kac labelings. Moreover, we compute the group of connected components \pi_0 G(R) of the real Lie group G(R) and the maps in exact sequences containing \pi_0 G(R) and H^1(R,G).
Keywords
Cite
@article{arxiv.2110.13062,
title = {Galois cohomology and component group of a real reductive group},
author = {Mikhail Borovoi and Dmitry A. Timashev},
journal= {arXiv preprint arXiv:2110.13062},
year = {2024}
}
Comments
V.1: 35 pages, v.2: 41 pages, v.3 41 pages