Abstract
Novikov algebras were introduced in connection with hydrodynamic-type Poisson brackets and Hamiltonian operators in the formal variational calculus. We have given a kind of realization of transitive Novikov algebras through the Novikov algebras given by S Gelfand and their compatible infinitesimal deformations in Bai and Meng (2001 J. Phys. A: Math. Gen. 34 3363-72). As a further and continuous study, we extend this realization theory to the non-transitive Novikov algebras in the paper. In two and three dimensions, we find that all non-transitive Novikov algebras also can be realized as the Novikov algebras given by S Gelfand and their compatible infinitesimal deformations. Moreover, they have simpler formulae.
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