Poisson-Lie T-Duality and Bianchi Type Algebras

Abstract

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.