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Abstract
We generalize Lie bialgebras and Lie bialgebioids to new objects which we call generalized Lie bialgebras. Similar to Lie bialgebras and Lie bial-gebroids, generalized Lie bialgebras are self-dual and generate canonically Hamiltonian structures on their representative spaces. We show that for a generalized Lie bialgebra (E, Ē), a pair (L 1,L 2) of E +Ē is again a generalized Lie bialgebra iff (L 1,L 2) is a Dirac structure pair . Construction of generalized Lie bialgebras by using Poisson tensors and Hamiltonian operators are also discussed in detail and an example relating to an infinite-dimensional integrable system is given.
