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arXiv · 1502.02770

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

Yanyong Hong
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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.

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Yanyong Hong. 2015-02-10. Central extensions and conformal derivations of a class of Lie conformal algebras. https://arxiv.org/abs/1502.02770

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