13 citations · 16 across the 11 of their papers we have counts for
5 papers · 1 filter
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…