# Quadratic Lie conformal superalgebras related to Novikov superalgebras

### Pavel S. Kolesnikov

Sobolev Institute of Mathematics, Novosibirsk, Russia### Roman A. Kozlov

Sobolev Institute of Mathematics, Novosibirsk; and Novosibirsk State University, Russia### Aleksander S. Panasenko

Sobolev Institute of Mathematics, Novosibirsk; and Novosibirsk State University, Russia

## Abstract

We study quadratic Lie conformal superalgebras associated with Novikov superalgebras. For every Novikov superalgebra $(V,\circ)$, we construct an enveloping differential Poisson superalgebra $U(V)$ with a derivation $d$ such that $u\circ v=ud(v)$ and $\{u,v\}=u\circ v-(-1)^{|u||v|}v\circ u$ for $u,v\in V$. The latter means that the commutator Gelfand–Dorfman superalgebra of $V$ is special. Next, we prove that every quadratic Lie conformal superalgebra constructed on a finite-dimensional special Gelfand–Dorfman superalgebra has a finite faithful conformal representation. This statement is a step towards a solution of the following open problem: whether a finite Lie conformal (super)algebra has a finite faithful conformal representation.

## Cite this article

Pavel S. Kolesnikov, Roman A. Kozlov, Aleksander S. Panasenko, Quadratic Lie conformal superalgebras related to Novikov superalgebras. J. Noncommut. Geom. 15 (2021), no. 4, pp. 1485–1500

DOI 10.4171/JNCG/445