Geodesic
Underlying Lie algebras of quadratic Novikov algebras
Czechoslovak Mathematical Journal, Tome 61 (2011) no. 2, pp. 323-328
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Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic type and the Hamiltonian operators in formal variational calculus. In this note we prove that the underlying Lie algebras of quadratic Novikov algebras are 2-step nilpotent. Moreover, we give the classification up to dimension $10$.
Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic type and the Hamiltonian operators in formal variational calculus. In this note we prove that the underlying Lie algebras of quadratic Novikov algebras are 2-step nilpotent. Moreover, we give the classification up to dimension $10$.
DOI : 10.1007/s10587-011-0077-z
Classification : 17A30, 17B30
Keywords: Novikov algebra; quadratic Novikov algebra; underlying Lie algebra 
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Chen, Zhiqi. Underlying Lie algebras of quadratic Novikov algebras. Czechoslovak Mathematical Journal, Tome 61 (2011) no. 2, pp. 323-328. doi: 10.1007/s10587-011-0077-z

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