eng
episciences.org
Communications in Mathematics
1804-1388
2336-1298
2023-01-03
Volume 30 (2022), Issue 3...
10.46298/cm.9298
9298
journal article
Galois cohomology of reductive algebraic groups over the field of real numbers
Mikhail Borovoi
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.
https://cm.episciences.org/9298/pdf
Mathematics - Group Theory
Mathematics - Number Theory
11E72, 20G20