Abstract
Using results of Cartan, Matsumoto, and Casselman, we give a short proof of Timashev’s theorem computing the real component group \(\pi _0G({\mathbb {R}})\) of a connected reductive \({\mathbb {R}}\)-group G in terms of a maximal torus of G containing a maximal split torus.
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Acknowledgements
This note was conceived when the first-named author was a guest of the Laboratory of Mathematics of Orsay (Laboratoire de Mathématiques d’Orsay, Université Paris-Saclay). He is grateful to the Laboratory for hospitality and good working conditions.
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Borovoi, M., Gabber, O. A short proof of Timashev’s theorem on the real component group of a real reductive group. Arch. Math. 120, 9–13 (2023). https://doi.org/10.1007/s00013-022-01798-y
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DOI: https://doi.org/10.1007/s00013-022-01798-y