  Balinsky and Novikov showed that the affinization of a Novikov algebra
naturally defines a Lie algebra, a property that in fact characterizes the
Novikov algebra. It is also an instance of the operadic Koszul duality. In this
paper, we develop a bialgebra theory for the Novikov algebra, namely the
Novikov bialgebra, which is characterized by the fact that its affinization (by
a quadratic right Novikov algebra) gives an infinite-dimensional Lie bialgebra,
suggesting a Koszul duality for properads. A Novikov bialgebra is also
characterized as a Manin triple of Novikov algebras. The notion of Novikov
Yang-Baxter equation is introduced, whose skewsymmetric solutions can be used
to produce Novikov bialgebras and hence Lie bialgebras. Moreover, these
solutions also give rise to skewsymmetric solutions of the classical
Yang-Baxter equation in the infinite-dimensional Lie algebras from the Novikov
algebras.
