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GALOIS COHOMOLOGY OF REAL SEMISIMPLE GROUPS VIA KAC LABELINGS

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Abstract

For a connected semisimple group G over the field of real numbers ℝ, using a method of Onishchik and Vinberg, we compute the first Galois cohomology set H1(ℝ;G) in terms of Kac labelings of the affine Dynkin diagram of G.

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Authors and Affiliations

  1. Raymond and Beverly Sackler, School of Mathematical Sciences, Tel Aviv University, 6997801, Tel Aviv, Israel

    M. BOROVOI

  2. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Department of Higher Algebra, 119991, Moscow, Russia

    D. A. TIMASHEV

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  1. M. BOROVOI
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  2. D. A. TIMASHEV
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Correspondence to D. A. TIMASHEV.

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To the memory of Èrnest Borisovich Vinberg

M. Borovoi is partially supported by the Israel Science Foundation (grant 870/16)

D. A. Timashev is partially supported by the Russian Foundation for Basic Research (grant 20-01-00091)

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BOROVOI, M., TIMASHEV, D.A. GALOIS COHOMOLOGY OF REAL SEMISIMPLE GROUPS VIA KAC LABELINGS. Transformation Groups 26, 433–477 (2021). https://doi.org/10.1007/s00031-021-09646-z

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