Quadratic Leibniz conformal algebras

TL;DR

This paper introduces quadratic Leibniz conformal algebras, providing their algebraic characterization, construction methods, and analysis of their one-dimensional central extensions, including those of quadratic Lie conformal algebras.

Contribution

It offers a new algebraic characterization and construction techniques for quadratic Leibniz conformal algebras, along with their central extension classifications.

Findings

Characterization of Leibniz conformal algebras via three algebraic operations.

Construction methods for quadratic Leibniz conformal algebras.

Classification of one-dimensional central extensions.

Abstract

In this paper, we study a class of Leibniz conformal algebras called quadratic Leibniz conformal algebras. An equivalent characterization of a Leibniz conformal algebra $R=\mathbb{C}[\partial]V$ through three algebraic operations on $V$ are given. By this characterization, several constructions of quadratic Leibniz conformal algebras are presented. Moreover, one-dimensional central extensions of quadratic Leibniz conformal algebras are considered using some bilinear forms on $V$. In particular, we also study one-dimensional Leibniz central extensions of quadratic Lie conformal algebras.