10.46298/cm.9298
https://cm.episciences.org/9298
Borovoi, Mikhail
Mikhail
Borovoi
Galois cohomology of reductive algebraic groups over the field of real numbers
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.
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
episciences.org
Mathematics - Group Theory
Mathematics - Number Theory
11E72, 20G20
arXiv.org - Non-exclusive license to distribute
2022-06-11
2023-01-03
2023-01-03
eng
journal article
arXiv:1401.5913
10.48550/arXiv.1401.5913
2336-1298
https://cm.episciences.org/9298/pdf
VoR
application/pdf
Communications in Mathematics
Volume 30 (2022), Issue 3 (Special issue: in memory of Arkady Onishchik)
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