From the 1 of 10 linked papers with an AI index.
10 papers
Initial pre-algebras as a generalization of dendriform algebras
P. S. Kolesnikov, B. K. Sartayev
The paper defines and studies initial pre‑algebras for binary operads, provides an algorithm to obtain their defining relations, and constructs Gröbner–Shirshov bases and tree‑base…
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…
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…