28 citations · 61 across the 5 of their papers we have counts for
5 papers
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…
Wildness of the problem of classifying nilpotent Lie algebras of vector fields in four variables
V. M. Bondarenko, A. P. Petravchuk
Let be a field of characteristic zero. Let be the Lie algebra of all -derivations with the Lie bracket $[D_1, D_2]:=D_1D_2-D_…
Systems of subspaces of a unitary space
Vitalij M. Bondarenko, Vyacheslav Futorny, Tatiana Klimchuk +2
For a given poset, we consider its representations by systems of subspaces of a unitary space ordered by inclusion. We classify such systems for all posets for which an explicit cl…
Pairs of mutually annihilating operators
Vitalij M. Bondarenko, Tatiana G. Gerasimova, Vladimir V. Sergeichuk
Pairs (A,B) of mutually annihilating operators AB=BA=0 on a finite dimensional vector space over an algebraically closed field were classified by Gelfand and Ponomarev [Russian Mat…
The problems of classifying pairs of forms and local algebras with zero cube radical are wild
Genrich Belitskii, Vitalij M. Bondarenko, Ruvim Lipyanski +2
We prove that over an algebraically closed field of characteristic not two the problems of classifying pairs of sesquilinear forms in which the second is Hermitian, pairs of biline…