2015/02/10 by Hong, Yanyong
#17B40 #17B65 #17B68 #17B69 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1502.02770
A quadratic Lie conformal algebra corresponds to a Hamiltonian pair in \citeGD, 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 \citeX1. 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.