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Keywords:
Novikov algebra; quadratic Novikov algebra; underlying Lie algebra
Novikov algebra; quadratic Novikov algebra; underlying Lie algebra
Summary:
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 $10$.
References:
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