A. P. Petravchuk

activity

20172023

most citedWildness of the problems of classifying two-dimensional spaces of commuting linear operators and certain Lie algebras

7 citations · 10 across the 3 of their papers we have counts for

collaborators

3 papers

math.AC2023

Centralizers of linear and locally nilpotent derivations

L. Bedratyuk, Y. Chapovskyi, A. Petravchuk

Let $K$ be an algebraically closed field of characteristic zero, $A = K [x_{1}, \dots, x_{n}]$ the polynomial ring, $R = K (x_{1}, \dots, x_{n})$ the field of rational functions, and let $W_n(K)…

math.RT2020★ 3 cited

Pairs of commuting nilpotent operators with one-dimensional intersection of kernels and matrices commuting with a Weyr matrix

Vitalij M. Bondarenko, Vyacheslav Futorny, Anatolii P. Petravchuk +1

I.M. Gelfand and V.A. Ponomarev (1969) proved that the problem of classifying pairs (A,B) of commuting nilpotent operators on a vector space contains the problem of classifying an…

math.RT2017★ 7 cited

Wildness of the problems of classifying two-dimensional spaces of commuting linear operators and certain Lie algebras

Vyacheslav Futorny, Tetiana Klymchuk, Anatolii P. Petravchuk +1

For each two-dimensional vector space $V$ of commuting $n \times n$ matrices over a field $F$ with at least 3 elements, we denote by $V$ the vector space of all $…