

Algebras in Analysis
May 17, 2019 18:05–19:35, Moscow, Lomonosov Moscow State University, room 1320.






Analytic functionals, smash products, and homological epimorphisms
O. Yu. Aristov^{} 
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Abstract:
(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 ArensMichael 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 ArensMichael envelope can be decomposed into an iterated smash product of this class.

