U -duality extension of Drinfel'd double

Abstract

A family of algebras ϵn that extends the Lie algebra of the Drinfel'd double is proposed. This allows us to systematically construct the generalized frame fields EAI which realize the proposed algebra by means of the generalized Lie derivative, i.e., £EAEBI = -ABCECI. By construction, the generalized frame fields include a twist by a Nambu-Poisson tensor. A possible application to the non-Abelian extension of U-duality and a generalization of the Yang-Baxter deformation are also discussed.