U -duality extension of Drinfel’d double

Abstract

Abstract A family of algebras $\mathcal{E}_n$ that extends the Lie algebra of the Drinfel’d double is proposed. This allows us to systematically construct the generalized frame fields $E_A{}^I$ which realize the proposed algebra by means of the generalized Lie derivative, i.e., . 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.