Galois cohomology and component group of a real reductive group

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 π_0 G(R) of the real Lie group G(R) and the maps in exact sequences containing π_0 G(R) and H^1(R,G).

Theorems & Definitions (91)

• Definition 3: Borovoi-Memoir
• Theorem 5
• Remark 1.1
• Lemma 1.2: See, for instance, AW
• proof
• Corollary 1.3
• Definition 1.5
• Lemma 1.6: obvious
• Definition 1.7
• Corollary 1.8: from Lemma \ref{['l:anti']}