Abstract
ABSTRACT A quadratic Lie conformal algebra corresponds to a Hamiltonian pair in Gel'fend and Dorfman (Hamiltonian operators and algebraic structures related to them. Funkts Anal Prilozhen. 1979;13:13–30), which plays fundamental roles in completely integrable systems. Moreover, it also corresponds to a certain compatible pair of a Lie algebra and a Novikov algebra which was called Gel'fand–Dorfman bialgebra by Xu (Quadratic conformal superalgebras. J Algebra. 2000;231:1–38). 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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