TY - JOUR
T1 - Galois cohomology of real quasi-connected reductive groups
AU - Borovoi, Mikhail
AU - Gornitskii, Andrei A.
AU - Rosengarten, Zev
N1 - Publisher Copyright:
© 2021, Springer Nature Switzerland AG.
PY - 2022/1
Y1 - 2022/1
N2 - 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.
AB - 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.
KW - Galois cohomology
KW - Quasi-connected reductive group
KW - Quasi-torus
KW - Real algebraic group
UR - http://www.scopus.com/inward/record.url?scp=85122496459&partnerID=8YFLogxK
U2 - 10.1007/s00013-021-01678-x
DO - 10.1007/s00013-021-01678-x
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AN - SCOPUS:85122496459
SN - 0003-889X
VL - 118
SP - 27
EP - 38
JO - Archiv der Mathematik
JF - Archiv der Mathematik
IS - 1
ER -