Abstract
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.
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