The analysis shows that completion homomorphisms are homological epimorphisms in complex Lie groups, implying broader algebraic structures can be examined.
It has been proved by the author [arXiv: 2404.19433] that the Arens-Michael envelope of a solvable Lie algebra is a homological epimorphism. We show here that for algebras of analytic functionals on a connected complex Lie group the analogous statement is satisfied without the assumption of solvability, and furthermore the completion homomorphisms of a more general form are also homological epimorphisms, including the envelope with respect to the class of Banach PI-algebras.
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Oleg Aristov (2025) studied this question.
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