Quadratic Lie conformal superalgebras related to Novikov superalgebras

We study quadratic Lie conformal superalgebras associated with Novikov superalgebras. For every Novikov superalgebra.V; ı/, we construct an enveloping differential Poisson superalgebra U.V/with a derivation d such that u o v = ud(v) and ¹u; v} u o v -.(-1)|u||v| vo u for u; v ∈ V. The latter means that the commutator Gelfand-Dorfman superalgebra of V is special. Next, we prove that every quadratic Lie conformal superalgebra constructed on a finite-dimensional special Gelfand-Dorfman superalgebra has a finite faithful conformal representation. This statement is a step towards a solution of the following open problem: whether a finite Lie conformal (super)algebra has a finite faithful conformal representation.