Galois cohomology of real quasi-connected reductive groups

Mikhail Borovoi*, Andrei A. Gornitskii, Zev Rosengarten

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

By a quasi-connected reductive group (a term of Labesse) over an arbitrary field we mean an almost direct product of a connected semisimple group and a quasi-torus (a smooth group of multiplicative type). We show that a linear algebraic group is quasi-connected reductive if and only if it is isomorphic to a smooth normal subgroup of a connected reductive group. We compute the first Galois cohomology set H1(R, G) of a quasi-connected reductive group G over the field R of real numbers in terms of a certain action of a subgroup of the Weyl group on the Galois cohomology of a fundamental quasi-torus of G.

Original languageEnglish
Pages (from-to)27-38
Number of pages12
JournalArchiv der Mathematik
Volume118
Issue number1
DOIs
StatePublished - Jan 2022

Funding

FundersFunder number
Moscow Center of Fundamental and Applied Mathematics075-15-2019-1621
Ministry of Education and Science of the Russian Federation
Israel Science Foundation870/16

    Keywords

    • Galois cohomology
    • Quasi-connected reductive group
    • Quasi-torus
    • Real algebraic group

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