Geodesic
Novikov–Poisson algebras and associative commutative derivation algebras
Algebra i logika, Tome 47 (2008) no. 2, pp. 186-202

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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.
Keywords: Novikov algebra, Lie algebra, derivation algebra, Jordan superalgebra. 
@article{AL_2008_47_2_a3,
     author = {V. N. Zhelyabin and A. S. Tikhov},
     title = {Novikov{\textendash}Poisson algebras and associative commutative derivation algebras},
     journal = {Algebra i logika},
     pages = {186--202},
     publisher = {mathdoc},
     volume = {47},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2008_47_2_a3/}
}
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V. N. Zhelyabin; A. S. Tikhov. Novikov–Poisson algebras and associative commutative derivation algebras. Algebra i logika, Tome 47 (2008) no. 2, pp. 186-202. http://geodesic.mathdoc.fr/item/AL_2008_47_2_a3/