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Central extensions and conformal derivations of a class of Lie conformal algebras
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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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On a class of infinite simple Lie conformal algebras
Determines central extensions, derivations, and modules for a class of infinite simple Lie conformal algebras from generalized Block type Lie algebras and proves they have no non-trivial finite conformal modules, henc...
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