We study the cohomological equation associated to linear cocycles on semi simple Lie groups over hyperbolic dynamics. We give sufficient conditions for the solution of the cohomological equation of fiber-bunched cocycles to be unique and for the Hölder conjugacy class of the cocycle to coincide with . In particular, we prove that there exists an open and dense subset of the set of fiber-bunched cocycles with trivial centralizer. As a consequence we deduce that the solutions of the {cohomological} equation of fiber-bunched cocycles form a finite abelian subgroup of for an open and dense subset of fiber-bunched cocycles in . Some results on the centralizer of skew-products are also given.
Paulo Varandas, On the cohomology class of fiber-bunched cocycles on semi simple Lie groups. Rev. Mat. Iberoam. 36 (2020), no. 4, pp. 1113–1132
DOI 10.4171/RMI/1160