Transitive Novikov Algebras on Four-Dimensional Nilpotent Lie Algebras

Research paper by Chengming Bai, Daoji Meng

Indexed on: 01 Oct '01Published on: 01 Oct '01Published in: International Journal of Theoretical Physics


Novikov algebras were introduced in connection with the Poisson brackets (of hydrodynamic type) and Hamiltonian operators in the formal variational calculus. The commutator of a Novikov algebra is a Lie algebra, and the radical of a finite-dimensional Novikov algebra is transitive. In this paper, we give a classification of transitive Novikov algebras on four-dimensional nilpotent Lie algebras based on Kim (1986, Journal of Differential Geometry24, 373–394).