Central extensions and conformal derivations of a class of Lie conformal algebras

Abstract

A quadratic Lie conformal algebra corresponds to a Hamiltonian pair in \cite{GD}, which plays fundamental roles in completely integrable systems. Moreover, it also corresponds to certain compatible pairs of a Lie algebra and a Novikov algebra which was called Gel'fand-Dorfman bialgebra by Xu in \cite{X1}. In this paper, central extensions and conformal derivations of quadratic Lie conformal algebras are studied in terms of Gel'fand-Dorfman bialgebras. It is shown that central extensions and conformal derivations of a quadratic Lie conformal algebra are related with some bilinear forms and some operators of the corresponding Gel'fand-Dorfman bialgebra respectively.

21 pages. We add some results on the central extensions of quadratic Lie conformal algebras by a one-dimensional center $\mathbb{C}{\mathfrak{c}}_{\beta }$ and an abelian Lie conformal algebra $\mathbb{C}[\partial ]\mathfrak{c}$ which is free of rank one

References in corpus (3)

• Loop Virasoro Lie Conformal Algebra
• Loop Schrödinger-Virasoro Lie conformal algebra
• The Lie conformal algebra of a Block type Lie algebra

Cited by in corpus (7)

• A new class of Z-graded Lie conformal algebras of infinite rank
• On Schrödinger-Virasoro type Lie conformal algebras
• Quadratic Leibniz conformal algebras
• Simplicity of quadratic Lie conformal algebras
• Super Hom-Gel'fand-Dorfman bialgebras and Hom-Lie conformal superalgebras
• Loop W(a,b) Lie conformal algebra
• On a class of infinite simple Lie conformal algebras