Galois cohomology of real quasi-connected reductive groups

Mikhail Borovoi, Andrei A. Gornitskii, Zev Rosengarten

Research output: Contribution to journalArticlepeer-review


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
Issue number1
StatePublished - Jan 2022


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


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