A short proof of Timashev’s theorem on the real component group of a real reductive group

Mikhail Borovoi; Ofer Gabber

doi:10.1007/s00013-022-01798-y

A short proof of Timashev’s theorem on the real component group of a real reductive group

Mikhail Borovoi^*, Ofer Gabber

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

Using results of Cartan, Matsumoto, and Casselman, we give a short proof of Timashev’s theorem computing the real component group πG(R) of a connected reductive R-group G in terms of a maximal torus of G containing a maximal split torus.

Original language	English
Journal	Archiv der Mathematik
DOIs	https://doi.org/10.1007/s00013-022-01798-y
State	Accepted/In press - 2022

Keywords

Maximal split torus
Real component group
Real reductive group

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10.1007/s00013-022-01798-y

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title = "A short proof of Timashev{\textquoteright}s theorem on the real component group of a real reductive group",

abstract = "Using results of Cartan, Matsumoto, and Casselman, we give a short proof of Timashev{\textquoteright}s theorem computing the real component group πG(R) of a connected reductive R-group G in terms of a maximal torus of G containing a maximal split torus.",

keywords = "Maximal split torus, Real component group, Real reductive group",

author = "Mikhail Borovoi and Ofer Gabber",

note = "Publisher Copyright: {\textcopyright} 2022, Springer Nature Switzerland AG.",

year = "2022",

doi = "10.1007/s00013-022-01798-y",

language = "אנגלית",

journal = "Archiv der Mathematik",

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T1 - A short proof of Timashev’s theorem on the real component group of a real reductive group

AU - Borovoi, Mikhail

AU - Gabber, Ofer

PY - 2022

Y1 - 2022

N2 - Using results of Cartan, Matsumoto, and Casselman, we give a short proof of Timashev’s theorem computing the real component group πG(R) of a connected reductive R-group G in terms of a maximal torus of G containing a maximal split torus.

AB - Using results of Cartan, Matsumoto, and Casselman, we give a short proof of Timashev’s theorem computing the real component group πG(R) of a connected reductive R-group G in terms of a maximal torus of G containing a maximal split torus.

KW - Maximal split torus

KW - Real component group

KW - Real reductive group

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U2 - 10.1007/s00013-022-01798-y

DO - 10.1007/s00013-022-01798-y

M3 - מאמר

AN - SCOPUS:85142129848

JO - Archiv der Mathematik

JF - Archiv der Mathematik

SN - 0003-889X

ER -

A short proof of Timashev’s theorem on the real component group of a real reductive group

Abstract

Keywords

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