Abstract
We study two-step nilpotent quadratic Lie algebras from the point of view of double extensions and T∗-extensions. As a consequence, an isometrically isomorphic classification of two-step nilpotent quadratic Lie algebras can be obtained from the classification of 3-vectors. Next, we apply the study of two-step nilpotent quadratic Lie algebras to the classification of non-commutative symmetric Novikov algebras. We focus on the 8-dimensional case and give some examples which are indecomposable and not solvable.
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