Computing Galois cohomology of a real linear algebraic group

Abstract

AbstractLet be a linear algebraic group, not necessarily connected or reductive, over the field of real numbers . We describe a method, implemented on computer, to find the first Galois cohomology set . The output is a list of 1‐cocycles in . Moreover, we describe an implemented algorithm that, given a 1‐cocycle , finds the cocycle in the computed list to which is equivalent, together with an element of realizing the equivalence.