Quadratic Leibniz conformal algebras

In this paper, we study a class of Leibniz conformal algebras called quadratic Leibniz conformal algebras. An equivalent characterization of a Leibniz conformal algebra [Formula: see text] through three algebraic operations on [Formula: see text] is 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 [Formula: see text]. In particular, we also study one-dimensional Leibniz central extensions of quadratic Lie conformal algebras.