Galois cohomology and component group of a real reductive group
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866913527451615232 |
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| author | Borovoi, Mikhail Timashev, Dmitry A. |
| author_facet | Borovoi, Mikhail Timashev, Dmitry A. |
| contents | Let G be a connected reductive group over the field of real numbers R. Using results of our previous joint paper, we compute combinatorially the first Galois cohomology set H^1(R,G) in terms of reductive Kac labelings. Moreover, we compute the group of connected components π_0 G(R) of the real Lie group G(R) and the maps in exact sequences containing π_0 G(R) and H^1(R,G). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_13062 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Galois cohomology and component group of a real reductive group Borovoi, Mikhail Timashev, Dmitry A. Group Theory Algebraic Geometry Number Theory Representation Theory Primary: 11E72, 20G10, 20G20 Let G be a connected reductive group over the field of real numbers R. Using results of our previous joint paper, we compute combinatorially the first Galois cohomology set H^1(R,G) in terms of reductive Kac labelings. Moreover, we compute the group of connected components π_0 G(R) of the real Lie group G(R) and the maps in exact sequences containing π_0 G(R) and H^1(R,G). |
| title | Galois cohomology and component group of a real reductive group |
| topic | Group Theory Algebraic Geometry Number Theory Representation Theory Primary: 11E72, 20G10, 20G20 |
| url | https://arxiv.org/abs/2110.13062 |