Classification of Novikov algebras

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Abstract

We describe a method for classifying the Novikov algebras with a given associated Lie algebra. Subsequently we give the classification of the Novikov algebras of dimension 3 over $\mathbb{R }$ and $\mathbb{C }$ , as well as the classification of the 4-dimensional Novikov algebras over $\mathbb{C }$ whose associated Lie algebra is nilpotent. In particular this includes a list of all 4-dimensional commutative associative algebras over $\mathbb{C }$ .

The first author was supported by the FWF, Projekt P21683. The second author thanks the ESI, Wien, for its hospitality and support.