The Bialgebraic Structure Of Two Kinds Of Lie Algebras Of Finite Dimension Related To Sl2

Lie bialgebra is a Lie algebra and a Lie coalgebra with a compatible structure of two mul-tiplications.Lie bialgebra which usually connects with Yang-Baxter equation,has been a powerful tool to study quantum group.Schr???dinger algebra and conformal Galilei algebra are two type of finite dimensional Lie algebras related to physics,3-dimensional simple Lie algebra sl₂is their subalgebra.In this paper,Lie bialgebras structures on Schr???dinger algebra and conformal Galilei algebra are studied.It is proved that all such Lie bialgebras are triangular coboundary.