GENERALIZED LIE BIALGEBRAS

We generalize Lie bialgebras and Lie bialgebroids to new objects which we call generalized Lie bialgebras. Similar to Lie bialgebras and Lie bialgebroids, generalized Lie bialgebras are self-dual and generate c anonically Hamiltonian structures on their representative spaces. We s how that for a generalized Lie bialgebra (E, (E) over bar), a pair (L- 1, L-2) of E + (E) over bar is again a generalized Lie bialgebra iff ( L-1, L2) is a Dirac structure pair. Construction of generalized Lie bi algebras by using Poisson tensors and Hamiltonian operators are also d iscussed in detail and an example relating to an infinite-dimensional integrable system is given.