8 citations · 27 across the 14 of their papers we have counts for
14 papers
Finitely -generated associative and Hopf algebras
Oleg Aristov
We introduce finitely -generated algebras, which can be treated as `algebras of functions' on non-commutative -differentiable spaces. Our approach uses the cate…
On density of polynomials in the algebra of holomorphic functions of exponential type on a linear Lie group
Oleg Aristov
It is shown by the author in [J. Lie Theory 29:4, 1045-1070, 2019] that for every connected linear complex Lie group the algebra of polynomials (regular functions) is dense in the…
Decomposition of the algebra of analytic functionals on a connected complex Lie group and its completions into iterated analytic smash products
Oleg Aristov
We show that a decomposition of a complex Lie group into a semidirect product generates that of the algebra of analytic functional, , into an analytic smash pr…
Length functions exponentially distorted on subgroups of complex Lie groups
Oleg Aristov
We introduce a notion of a length function exponentially distorted on a (compactly generated) subgroup of a locally compact group. We prove that for a connected linear complex Lie…
Holomorphic reflexivity for locally finite and profinite groups: the abelian and general cases
Oleg Aristov
Akbarov's theory of holomorphic reflexivity for topological Hopf algebras has been developed in two directions, namely, by the complication of definitions when expanding the scope…
Functions of class in non-commuting variables in the context of triangular Lie algebras
Oleg Aristov
We construct a certain completion of the universal enveloping algebra of a triangular real Lie algebra . It is a Fréchet-Arens-Michael algebra…
Banach space representations of Drinfeld-Jimbo algebras and their complex-analytic forms
Oleg Aristov
We prove that every non-degenerate Banach space representation of the Drinfeld-Jimbo algebra of a semisimple complex Lie algebra is finite dimens…
Holomorphically finitely generated Hopf algebras and quantum Lie groups
Oleg Aristov
We study topological Hopf algebras that are holomorphically finitely generated (HFG) as Fréchet Arens--Micheal algebras in the sense of Pirkovskii. Some of them, but not all, can b…
On holomorphic reflexivity conditions for complex Lie groups
Oleg Aristov
We consider Akbarov's holomorphic version of the non-commutative Pontryagin duality for a complex Lie group. We prove, under the assumption that is a Stein group with finitely…
The relation "commutator equals function'' in Banach algebras
Oleg Aristov
The relation , where is a holomorphic function, occurs naturally in the definitions of some quantum groups. To attach a rigorous meaning to the right-hand side of t…
Holomorphic functions of exponential type on connected complex Lie groups
Oleg Aristov
Holomorphic functions of exponential type on a complex Lie group (introduced by Akbarov) form a locally convex algebra, which is denoted by $\cO_{exp}(G)$. Our aim is to descri…
Arens-Michael envelopes of nilpotent Lie algebras, holomorphic functions of exponential type, and homological epimorphisms
Oleg Aristov
Our aim is to give an explicit description of the Arens-Michael envelope for the universal enveloping algebra of a finite-dimensional nilpotent complex Lie algebra. It turns out th…
Topological radical of Banach module
Oleg Aristov
We introduce the concept of topological radical of a Banach module. This closed submodule have two description: the as the intersection of ranges of maximal contractive monomorphis…
Operator biflatness of the Fourier algebra and approximate indicators for subgroups
Oleg Yu. Aristov, Volker Runde, Nico Spronk
We investigate if, for a locally compact group , the Fourier algebra is biflat in the sense of quantized Banach homology. A central role in our investigation is played by…