13 citations · 16 across the 11 of their papers we have counts for
12 papers
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…
On the structure of finite Novikov conformal algebras
Pavel Kolesnikov, Jiefeng Liu
We classify finite simple Novikov conformal algebras over an algebraically closed field of characteristic zero. The classification consists of the current conformal algebra over th…
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…
Chiral algebras with abelian conformal part
I. V. Dudin, P. S. Kolesnikov
We study a categorical approach to the concept of varieties of chiral algebras. We prove that the class of chiral algebras in the variety defined by a binary quadratic operad Var,…
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 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…
Hochschild cohomology of the universal associative conformal envelope of the Virasoro Lie conformal algebra with coefficients in all finite modules
Hassan Alhussein, Pavel Kolesnikov, Viktor Lopatkin
In this paper, we find the Hochschild cohomology groups of the universal associative conformal envelope of the Virasoro Lie conformal algebra with respect to associative loc…
On the pre-commutative envelopes of commutative algebras
H. Alhussein, P. Kolesnikov
We prove that every nilpotent commutative algebra can be embedded into a pre-commutative (Zinbiel) algebra with respect to the anti-commutator operation. For finite-dimensional alg…
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…
Formal integration of complete Rota-Baxter Lie algebras
Maxim Goncharov, Pavel Kolesnikov, Yunhe Sheng +1
In this paper, first we revisit the formal integration of Lie algebras, which give rise to braces in some special cases. Then we establish the formal integration theory for complet…
Groebner--Shirshov bases method for vertex algebras
R. A. Kozlov, P. S. Kolesnikov
In this note we show how to apply the Gröbner--Shirshov bases (GSB) method for modules over an associative algebra to the study of vertex algebras defined by generators and relatio…
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…