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All Bianchi bialgebras have been obtained. By introducing a non-degenerate
adjoint invariant inner product over these bialgebras the associated
Drinfeld doubles have been constructed, then by calculating the coupling
matrices for these bialgebras several $\sigma$-models with Poisson-Lie
symmetry have been obtained. Two simple examples as prototypes of
Poisson-Lie dual models have been given.
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