Galois cohomology of real semisimple groups

2015/06/20 by Mikhail Borovoi, Borovoi, Mikhail, Dmitry A. Timashev +1 · 2 citations
Mathematics · #11E72 #20G10 #20G20 #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic number #Cohomology #Discrete mathematics #FOS: Mathematics #Field (mathematics) #Galois cohomology #Galois group #Galois module #Group (periodic table) #Group Theory (math.GR) #Group cohomology #Homotopy and Cohomology in Algebraic Topology #Mathematical analysis #Mathematics #Number Theory (math.NT) #Physics #Pure mathematics #Type (biology) #math.AG #math.GR #math.NT #msc:11E72 #msc:20G10 #msc:20G20

paper · pdf · doi:10.48550/arxiv.1506.06252

published in arXiv (Cornell University) (Cornell University) · 16 pages

arxiv created 2015/06/20 · openalex publication_date 2015/06/20 · arxiv updated 2015/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Let G be a connected, compact, semisimple algebraic group over the field of real numbers R. Using Kac diagrams, we describe combinatorially the first Galois cohomology sets H¹(R,H) for all inner forms H of G. As examples, we compute explicitly H¹ for all real forms of the simply connected group of type E₇ (which has been known since 2013) and for all real forms of half-spin groups of type D_2k (which seems to be new).

Cited by

• Galois cohomology of real semisimple groups via Kac labelings

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• Galois cohomology of real semisimple groups via Kac labelings
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