Hochshild's method for describing the Mackenzie obstruction for construction of transitive Lie algebroid

The technique developed in Hochschild’s works "Lie algebra kernels and cohomology " and "Cohomology classes of finite dimensional kernels for Lie algebras " [2],[3] can be applied to the special case of transitive Lie algebroids. Our task is formulated to transfer the Hochschild construction to the case of transitive Lie algebroids and prove a similar theorem.