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 describe 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 realizing the equivalence.
Computing Galois cohomology of a real linear algebraic group / Borovoi, Mikhail; de Graaf, Willem A.. - In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6107. - 109:5(2024), pp. e1290601-e1290653. [10.1112/jlms.12906]
Computing Galois cohomology of a real linear algebraic group
de Graaf, Willem A.
2024-01-01
Abstract
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 describe 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 realizing the equivalence.File | Dimensione | Formato | |
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Journal of London Math Soc - 2024 - Borovoi - Computing Galois cohomology of a real linear algebraic group.pdf
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