Noncommutative Novikov algebras

Abstract

The class of Novikov algebras is a popular object of study among classical nonassociative algebras. A generic example of a Novikov algebra may be constructed from an associative and commutative algebra A with a derivation d: it is enough to consider the operation $$a\,{\circ }\, b = ad(b)$$ , $$a,b\in A$$ , on the same space A. We consider a more general class of linear algebras which may be obtained in the same way from not necessarily commutative associative algebras with a derivation.