Simplicity of quadratic Lie conformal algebras

In this paper, simplicity of quadratic Lie conformal algebras are investigated. From the point view of the corresponding Gel'fand-Dorfman bialgebras, some sufficient conditions and necessary conditions to ensure simplicity of quadratic Lie conformal algebras are presented. By these observations, we present several classes of new infinite simple Lie conformal algebras. These results will be useful for classification purposes.