Vladimir Dotsenko

activity

20242026

collaborators

5 papers

math.RT2026

Young's lattice, invariant ideals, and weak identities

Vladimir Dotsenko, Artem Lopatin

For a $d$ -dimensional vector space $V$ over a field of characteristic zero, we show that $G L (V)$ -stable ideals of the universal enveloping algebra of the free two-step nilpotent Li…

math.RA2026

A Nielsen--Schreier variety of algebras without the PBW property

Vladimir Dotsenko, Bekzat Zhakhayev

We prove the Nielsen--Schreier property for the variety of algebras defined by the identity $x (x^{2})^{2} = (x^{2})^{2} x$ : every subalgebra of every free algebra in this variety is itself fr…

math.RA2025

Derived operations satisfy standard identities

Vladimir Dotsenko

A derived operation is a bilinear operation on a commutative associative algebra $A$ defined intrinsically out of its product and several derivations of the product. We show that o…

math.RA2024

Distributive lattices of varieties of Novikov algebras

Vladimir Dotsenko, Bekzat Zhakhayev

We prove that a variety of Novikov algebras has a distributive lattice of subvarieties if and only if the lattice of its subvarieties defined by identities of degree three is distr…

math.RT2024

Categorification of quiver diagonalization and Koszul algebras

Vladimir Dotsenko, Evgeny Feigin, Piotr Kucharski +1

In earlier work of three of the authors of the present paper, a supercommutative quadratic algebra was associated to each symmetric quiver, and a new proof of positivity of motivic…