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A Lie algebraic approach to Novikov algebras. (English) Zbl 1033.17001
Summary: Novikov algebras were introduced in connection with Poisson brackets of hydrodynamic type and Hamiltonian operators in the formal variational calculus. The commutator of a Novikov algebra is a Lie algebra. Thus it is useful to relate the study of Novikov algebras to the theory of Lie algebras. In this paper, we realize Novikov algebras through a Lie algebraic approach. Such a realization could be important in physics and geometry. We find that all transitive Novikov algebras in dimension 3 can be realized as the Novikov algebras obtained through Lie algebras and their compatible linear (global) deformations.
17A30Nonassociative algebras satisfying other identities
55N35Other homology theories (algebraic topology)
55Q70Homotopy groups of special types