Computing Galois cohomology of a real linear algebraic group
arXiv:2308.04962 · doi:10.1112/jlms.12906
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 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.
V1: 41 pages. V2: 45 pages, the final version to appear in J. London Math. Soc