Lie Bialgebras of Generalized Witt Type 10471091 of China, Two Grants " Excellent Young Teacher Program " and " Trans-century Training Programme Foundation for the Talents " from Ministry of Education of China

Guang’ai Song and Yucai Su Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, China E-mail: [email protected], [email protected] Abstract. In a paper by Michaelis a class of infinite-dimensional Lie bialgebras containing the Virasoro algebra was presented. This type of Lie bialgebras was classified by Ng and Taft. In this paper, all Lie bialgebra structures on the Lie algebras of generalized Witt type are classified. It is proved that, for any Lie algebra W of generalized Witt type, all Lie bialgebras on W are coboundary triangular Lie bialgebras. As a by-product, it is also proved that the first cohomology group H1(W,W ⊗W) is trivial.