Analytic functionals, smash products, and homological epimorphisms

(This is a continuation of the talk of September 28, 2018). We discuss the proof of the following theorem: for each connected complex Lie group, the Arens-Michael envelope of the algebra of analytic functionals is a homological epimorphism.
Afterr recalling the necessary definitions, we concentrate on constructing a free resolution needed for the proof of our result. This construction is used in the group cohomology theory in the case of a semidirect product. We adapt it to the setting of analytic smash products under the action of a cocommutative topological Hopf algebra. Remarkably, not only the algebra of analytic functionals, but also its Arens-Michael envelope can be decomposed into an iterated smash product of this class.