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 \(\mathbb{C }\).
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The first author was supported by the FWF, Projekt P21683. The second author thanks the ESI, Wien, for its hospitality and support.
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Burde, D., de Graaf, W. Classification of Novikov algebras. AAECC 24, 1–15 (2013). https://doi.org/10.1007/s00200-012-0180-x
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DOI: https://doi.org/10.1007/s00200-012-0180-x