A. Petravchuk

activity

20062026

most citedOn closed rational functions in several variables

10 citations · 21 across the 18 of their papers we have counts for

collaborators

18 papers

math.RA2026

A family of maximal subalgebras of the Lie algebra~ $W_{n} (K)$

Y. Chapovskyi, A. Petravchuk

Let $K$ be an algebraically closed field of characteristic zero and $P_{n} = K [x_{1}, \dots, x_{n}]$ the polynomial ring. Any $K$ -derivation $D$ on $P_{n}$ is of the form ${ D=\sum_{i=1}^n…

math.RT2024

Polynomial similarity of pairs of matrices

Vitaliy Bondarenko, Anatoliy Petravchuk, Maryna Styopochkina

Let $K$ be a field, $R = K [x, y]$ the polynomial ring and $M (K)$ the set of all pairs of square matrices of the same size over $K .$ Pairs $P_{1} = (A_{1}, B_{1})$ and $P_2=(A_2,B_2)…

math.RA2023

Centralizers of Jacobian derivations

D. I. Efimov, A. P. Petravchuk, M. S. Sydorov

Let $K$ be an algebraically closed field of characteristic zero, $K [x, y]$ the polynonial ring in variables $x$ , $y$ and let $W_{2} (K)$ be the Lie algebra of…

math.RA2022★ 1 cited

Automorphisms and derivations of affine commutative and PI-algebras

Oksana Bezushchak, Anatoliy Petravchuk, Efim Zelmanov

We prove analogs of A.~Selberg's result for finitely generated subgroups of $Aut (A)$ and of Engel's theorem for subalgebras of $Der (A)$ for a finitely generated assoc…

math.RA2018★ 1 cited

Wildness of the problem of classifying nilpotent Lie algebras of vector fields in four variables

V. M. Bondarenko, A. P. Petravchuk

Let $F$ be a field $F$ of characteristic zero. Let $W_{n} (F)$ be the Lie algebra of all $F$ -derivations with the Lie bracket $[D_1, D_2]:=D_1D_2-D_…

math.RA2017★ 1 cited

On Lie algebras associated with modules over polynomial rings

A. P. Petravchuk, K. Ya. Sysak

Let $K$ be an algebraically closed field of characteristic zero. Let $V$ be a module over the polynomial ring $K [x, y]$ . The actions of $x$ and $y$ determine linear…