22 citations · 48 across the 14 of their papers we have counts for
17 papers
Special identities of nonsymmetric bicommutative operations in associative algebra with an operator
Bauyrzhan Sartayev, Abdibek Ydyrys
Let be an associative non-unital algebra with a linear operator satisfying \[aS(S(b)c)=S(aS(b))c,\] and define and . We determine the speci…
A unified approach to the definition of anti-algebras
Ivan Kaygorodov, Abror Khudoyberdiyev, Bauyrzhan Sartayev
We introduce the arseille anti-construction for varieties of algebras defined by multilinear identities of degree , obtained by changing the sign of…
The Weight Criterion, Dong Property, and Manin Products of Operads
P. Kolesnikov, B. Sartayev
We establish that, for a binary operad Var, the Hadamard product of Var and the operad Nov of Novikov algebras is a binary operad (i.e., coincides with their Manin white product No…
Initial pre-algebras as a generalization of dendriform algebras
P. S. Kolesnikov, B. K. Sartayev
We continue the study of \emph{initial dialgebras} defined in~\cite{DMS2026}. For a binary operad $\Var$ we define the class of initial pre-$\Var$-algebras and the corresponding op…
Malcev classification for the variety of left-symmetric algebras
A. Ryskeldin, B. Sartayev
In this paper, we study three classes of subvarieties inside the variety of left-symmetric algebras. We show that these subvarieties are naturally related to some well-known variet…
Free Algebras in Mal'cev-Type Subvarieties of Associative Algebras
B. Sartayev, A. Ydyrys
In this paper, we study free algebras in subvarieties of the variety of associative algebras singled out by Mal'cev's classification. For each subvariety, we construct the bases fo…
4-type subvarieties of the variety of associative algebras
A. Kunanbayev, B. Sartayev
In this paper, we consider four types of subvarieties of the variety of associative algebras. We study these subvarieties from the point of view of operads and show their connectio…
White Manin product and Hadamard product
P. S. Kolesnikov, B. K. Sartayev
In this paper, we consider three types of operads: alternative, assosymmetric, and bicommutative. We prove that the Hadamard product of these operads with the Novikov operad coinci…
On the differential Novikov algebras
A. Dauletiyarova, B. Sartayev
We study the quadratic operad $\Der\Nov_q$ determined by the degree- identities arising from the operad $\Nov\circ\Nov$, and its quadratic dual $\Der\Nov^!$. We show that the na…
On the Dong Property for a binary quadratic operad
P. S. Kolesnikov, B. K. Sartayev
The classical Dong Lemma for distributions over a Lie algebra lies in the foundation of vertex algebras theory. In this paper, we find necessary and sufficient condition for a vari…
Basis of the free noncommutative Novikov algebra
B. K. Sartayev
As it is known, the defining identities of a free Novikov algebra can be obtained from a commutative algebra with a derivation. In this paper, we consider a class of algebras obtai…
Free special Gelfand-Dorfman algebra
V. Gubarev, B. K. Sartayev
A Gelfand-Dorfman algebra is called special if it can be embedded into a differential Poisson algebra. We find a new basis of the free Novikov algebra. With its help, we construct…
Noncommutative Novikov algebras
P. Kolesnikov, B. Sartayev
The class of Novikov algebras is a popular object of study among classical nonassociative algebras. The generic example of a Novikov algebra may be obtained from a differential ass…
Metabelian Lie and perm algebras
F. A. Mashurov, B. K. Sartayev
It is well known that any Lie algebra can be embedded into an associative algebra. We prove that any metabelian Lie algebra can be embedded into an algebra in the subvariety of per…
On the embedding of left-symmetric algebras into differential perm-algebras
P. S. Kolesnikov, B. K. Sartayev
Given an associative algebra satisfying the left commutativity identity (Perm-algebra) with a derivation , the new operation is left-symmetric (pre…
On the special identities of Gelfand--Dorfman algebras
P. S. Kolesnikov, B. K. Sartayev
In this paper, we prove that the class of all special Gelfand--Dorfman algebras (GD-algebras) is closed with respect to homomorphisms and thus forms a variety. We also prove that e…
Gelfand--Dorfman algebras, derived identities, and the Manin product of operads
P. S. Kolesnikov, B. Sartayev, A. Orazgaliev
Gelfand--Dorfman bialgebras (GD-algebras) are nonassociative systems with two bilinear operations satisfying a series of identities that express Hamiltonian property of an operator…