Linear extensions of dynamic systems and the reductibility problem

The relation of linear extensions of smooth dynamic systems to cohomologies and to reducibility in the case of flow is investigated. A result is obtained concerning -cohomologies in the neighborhood of a constant cocycle for the case of an arbitrary closed subgroup of the group GL (k, C).Translated from Matematicheskie Zametki, Vol. 8, No. 4, pp. 451–462, October, 1970.