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Quadratic Leibniz conformal algebras (1607.04936v2)
Published 18 Jul 2016 in math.QA and math.RA
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.