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Galois cohomology of reductive algebraic groups over the field of real numbers
- Source :
- Communications in Mathematics, Volume 30 (2022), Issue 3 (Special issue: in memory of Arkady Onishchik) (January 3, 2023) cm:9298
- Publication Year :
- 2014
-
Abstract
- We describe functorially the first Galois cohomology set $H^1({\mathbb R},G)$ of a connected reductive algebraic group $G$ over the field $\mathbb R$ of real numbers in terms of a certain action of the Weyl group on the real points of order dividing 2 of the maximal torus containing a maximal compact torus. This result was announced with a sketch of proof in the author's 1988 note. Here we give a detailed proof.<br />Comment: V.1, v.2, v.3: 6 pages. V.4, v.5: 11 pages, the final version to appear in Communicationa in Mathematics. In this final version, Theorem 9 (the main result) of versions 1-3 became Theorem 3.1
- Subjects :
- Mathematics - Group Theory
Mathematics - Number Theory
11E72, 20G20
Subjects
Details
- Database :
- arXiv
- Journal :
- Communications in Mathematics, Volume 30 (2022), Issue 3 (Special issue: in memory of Arkady Onishchik) (January 3, 2023) cm:9298
- Publication Type :
- Report
- Accession number :
- edsarx.1401.5913
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.46298/cm.9298