4 citations · 7 across the 6 of their papers we have counts for
7 papers
Homological dimensions of algebras of analytic functionals and their completions
Oleg Aristov
We show that the main homological dimensions of the algebra of analytic functionals on a connected complex Lie group, as well as some of its completions, coincide with the dimensio…
Algebras of analytic functionals and homological epimorphisms
Oleg Aristov
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 analy…
The Arens-Michael envelope of a solvable Lie algebra is a homological epimorphism
Oleg Aristov
The Arens-Michael envelope of the universal enveloping algebra of a finite-dimensional complex Lie algebra is a homological epimorphism if and only if the Lie algebra is solvable.…
When a completion of the universal enveloping algebra is a Banach PI-algebra?
Oleg Aristov
We prove that a Banach algebra that is a completion of the universal enveloping algebra of a finite-dimensional complex Lie algebra satisfies a polynomial identi…
The structure of the linearizer of a connected complex Lie group
Oleg Aristov
The Morimoto theorem states that each connected abelian complex Lie group can be decomposed into the direct product of a group on which all holomorphic functions are constant,…
Sheaves of non-commutative smooth and holomorphic functions associated with the non-abelian two-dimensional Lie algebra
Oleg Aristov
Dosi and, quite recently, the author showed that, on the character space of a nilpotent Lie algebra, there exists a sheaf of Fréchet--Arens--Michael algebras (of noncommutative hol…
An analytic criterion for the local finiteness of a countable semigroup
Oleg Aristov
We prove that a countable semigroup is locally finite if and only if the Arens-Michael envelope of its semigroup algebra is a -space. This is a counterpart to a recent re…