Novikov algebras and Schrödinger–Virasoro Lie algebras

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In this paper, we give realizations of the (twisted) Schrödinger–Virasoro Lie algebras and their certain deformations in terms of Novikov algebras. In particular, we obtain a nontrivial twisted generalization of the Balinsky–Novikov construction of certain infinite-dimensional Lie algebras from Novikov algebras. As applications, we show that the central extensions and the highest weight modules of the (twisted) Schrödinger–Virasoro Lie algebras are determined by the corresponding Novikov algebras.