Computing Galois cohomology of a real linear algebraic group

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.

arXiv commentV1: 41 pages. V2: 45 pages, the final version to appear in J. London Math. Soc

References in corpus (8)

• Generating Geodesic Flows and Supergravity Solutions
• Galois and Cartan Cohomology of Real Groups
• Galois cohomology of reductive algebraic groups over the field of real numbers
• Black hole solutions to the $F_4$-model and their orbits (I)
• Galois cohomology and component group of a real reductive group
• Approximation faible et principe de Hasse pour des espaces homogènes à stabilisateur fini résoluble (Weak Approximation and Hasse Principle for homogeneous spaces with finite solvable stabilizer)
• Equivariant models of spherical varieties
• Cohomological representations for real reductive groups