Quadratic Leibniz conformal algebras

Jinsen Zhou; Yanyong Hong

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Quadratic Leibniz conformal algebras

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arxiv 1607.04936 v2 pith:CWOTME2F submitted 2016-07-18 math.QA math.RA

Jinsen Zhou , Yanyong Hong This is my paper

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keywords conformalleibnizalgebrasquadraticcentralcharacterizationextensionsone-dimensional

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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.

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