V. Zhelyabin

collaborators

3 papers

math.RA2021

On the Lie-solvability of Novikov algebras

Kaisar Tulenbaev, Ualbai Umirbaev, Viktor Zhelyabin

We prove that any Novikov algebra over a field of characteristic $\neq = 2$ is Lie-solvable if and only if its commutator ideal $[N, N]$ is right nilpotent. We also construct examples…

math.RA2021

Some examples of nonassociative coalgebras and supercoalgebras

Daniyar Kozybaev, Ualbai Umirbaev, Viktor Zhelyabin

Locally finiteness of some varieties of nonassociative coalgebras is studied and the Gelfand-Dorfman construction for Novikov coalgebras and the Kantor construction for Jordan supe…

math.RA2020

A Dixmier theorem for Poisson enveloping algebras

Ualbai Umirbaev, Viktor Zhelyabin

We consider a skew-symmetric $n$ -ary bracket on the polynomial algebra $K [x_{1}, \dots, x_{n}, x_{n + 1}]$ ( $n \geq 2$ ) over a field $K$ of characteristic zero defined by $\{a_1,\ldots,a_n\…