U-duality extension of Drinfel'd double

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., $\hat{$\mathcal{L}$}{E_A}E_B{}^I = - $\mathcal{F}${AB}{}^C,E_C{}^I$. 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.