Gel'fand-Dorfman bialgebras (Q1879060)

A Gel'fand-Dorfman bialgebra is a vector space with a Lie algebra structure and a Novikov algebra structure, satisfying a certain compatibility condition. The bialgebra structure corresponds to certain Hamiltonian pairs in the Gel'fand-Dikii-Dorfman theory of Hamiltonian operators. Here the author gives a survey on the study of Gel'fand-Dorfman bialgebras, based upon his previously published contributions. No proofs are provided but the author refers to the literature. He starts with a more technical introduction to the bialgebras through what he calls ``Lie algebra with one-variable structure.