37 citations · 91 across the 9 of their papers we have counts for
10 papers
The symmetric operation in a free Novikov algebra
Askar Dzhumadil'daev, Nurlan Ismailov
We study the symmetrization of the Novikov product. Using the embedding of a free Novikov algebra into a commutative differential algebra over a field of characteristic zero, we fi…
On the generalized Poisson and transposed Poisson algebras
Askar Dzhumadil'daev, Nurlan Ismailov, Farukh Mashurov
We provide the polynomial identities of algebras that are both generalized Poisson algebras and transposed Poisson algebras. We establish defining identities via single operation f…
Free bicommutative superalgebras
Vesselin Drensky, Nurlan Ismailov, Manat Mustafa +1
We introduce the variety of bicommutative superalgebras over an arbitrary field of characteristic different from 2. The variety consists of all nonas…
Polynomial identities in Novikov algebras
Vladimir Dotsenko, Nurlan Ismailov, Ualbai Umirbaev
In this paper, we study Novikov algebras satisfying nontrivial identities. We show that a Novikov algebra over a field of zero characteristic that satisfies a nontrivial identity s…
The algebraic and geometric classification of nilpotent right alternative algebras
Nurlan Ismailov, Ivan Kaygorodov, Manat Mustafa
We present algebraic and geometric classifications of the -dimensional complex nilpotent right alternative algebras. Specifically, we find that, up to isomorphism, there are onl…
Unary and binary Leibniz algebras
N. A. Ismailov, A. S. Dzhumadil'daev
An algebra is said to be a unary Leibniz algebra if every one-generated subalgebra is a Leibniz algebra. An algebra is said to be a binary Leibniz algebra if every two-generated su…
On the speciality of Tortkara algebras
Askar Dzhumadil'daev, Nurlan Ismailov, Farukh Mashurov
A criterion for elements of free Zinbiel algebras to be Lie or Jordan is established. This criterion is used in studying speciality problems of Tortkara algebras. We construct a ba…
Degenerations of Leibniz and anticommutative algebras
Nurlan Ismailov, Ivan Kaygorodov, Yury Volkov
We describe all degenerations of three dimensional anticommutative algebras and of three dimensional Leibniz algebras over In…
Polynomial identities of bicommutative algebras, Lie and Jordan elements
A. S. Dzhumadil'daev, N. A. Ismailov
An algebra with identities is called bicommutative. We construct list of identities satisfied by commutator and anti-commutator products in a free bico…
The geometric classification of Leibniz algebras
Nurlan Ismailov, Ivan Kaygorodov, Yury Volkov
We describe all rigid algebras and all irreducible components in the variety of four dimensional Leibniz algebras over In particular, we prove tha…