Novikov–Poisson algebras and associative commutative derivation algebras

We describe Novikov–Poisson algebras in which a Novikov algebra is not simple while its corresponding associative commutative derivation algebra is differentially simple. In particular, it is proved that a Novikov algebra is simple over a field of characteristic not 2 iff its associative commutative derivation algebra is differentially simple. The relationship is established between Novikov–Poisson algebras and Jordan superalgebras.