81 citations · 388 across the 32 of their papers we have counts for
33 papers
On the locality of formal distributions over pre-Lie and Novikov algebras
L. A. Bokut, P. S. Kolesnikov
The Dong Lemma in the theory of vertex algebras states that the locality property of formal distributions over a Lie algebra is preserved under the action of a vertex operator. A~s…
Word problem for finitely presented metabelian Poisson algebras
Zerui Zhang, Yuqun Chen, L. A. Bokut
We first construct a linear basis for a free metabelian Poisson algebra generated by an arbitrary well-ordered set. It turns out that such a linear basis depends on the characteris…
On free Gelfand--Dorfman--Novikov superalgebras and a PBW type theorem
Zerui Zhang, L. A. Bokut, Yuqun Chen
We construct a linear basis of a free GDN superalgebra over a field of characteristic . As applications, we prove a PBW theorem, that is, any GDN superalgebra can be embedd…
On free Gelfand-Dorfman-Novikov-Poisson algebras and a PBW theorem
L. A. Bokut, Yuqun Chen, Zerui Zhang
In 1997, X. Xu \cite{Xiaoping Xu Poisson} invented a concept of Novikov-Poisson algebras (we call them Gelfand-Dorfman-Novikov-Poisson (GDN-Poisson) algebras). We construct a linea…
Gröbner-Shirshov bases method for Gelfand-Dorfman-Novikov algebras
L. A. Bokut, Yuqun Chen, Zerui Zhang
We establish Gröbner-Shirshov bases theory for Gelfand-Dorfman-Novikov algebras over a field of characteristic . As applications, a PBW type theorem in Shirshov form is given an…
Gröbner-Shirshov bases and PBW theorems
L. A. Bokut, Yuqun Chen
We review some applications of Gröbner-Shirshov bases, including PBW theorems, linear bases of free universal algebras, normal forms for groups and semigroups, extensions of groups…