Computing Galois cohomology of a real linear algebraic group
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916650441244672 |
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| author | Borovoi, Mikhail de Graaf, Willem A. |
| author_facet | Borovoi, Mikhail de Graaf, Willem A. |
| contents | Let G be a linear algebraic group, not necessarily connected or reductive, over the field of real numbers R. We describe a method, implemented on computer, to find the first Galois cohomology set H^1(R,G). The output is a list of 1-cocycles in G. Moreover, we have an implemented algorithm that, given a 1-cocycle z in Z^1(R,G), finds the cocycle in the computed list to which z is equivalent, together with an element of G(C) realizing the equivalence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_04962 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Computing Galois cohomology of a real linear algebraic group Borovoi, Mikhail de Graaf, Willem A. Representation Theory Algebraic Geometry Group Theory 20G10, 11E72, 20G20, 68W30 Let G be a linear algebraic group, not necessarily connected or reductive, over the field of real numbers R. We describe a method, implemented on computer, to find the first Galois cohomology set H^1(R,G). The output is a list of 1-cocycles in G. Moreover, we have an implemented algorithm that, given a 1-cocycle z in Z^1(R,G), finds the cocycle in the computed list to which z is equivalent, together with an element of G(C) realizing the equivalence. |
| title | Computing Galois cohomology of a real linear algebraic group |
| topic | Representation Theory Algebraic Geometry Group Theory 20G10, 11E72, 20G20, 68W30 |
| url | https://arxiv.org/abs/2308.04962 |