  A Drinfel'd algebra gives the systematic construction of generalized
parallelizable spaces and this allows us to study an extended T-duality, known
as the Poisson-Lie T-duality. Recently, in order to find a generalized
U-duality, an extended Drinfel'd algebra (ExDA), called the Exceptional
Drinfel'd algebra (EDA) was proposed and a natural extension of the usual
U-duality was studied both in the context of supergravity and membrane theory.
In this paper, we clarify the general structure of ExDAs and show that an ExDA
always gives a generalized parallelizable space, which may be regarded as a
group manifold with generalized Nambu-Lie structures. We also discuss
generalized Yang-Baxter deformations that are based on coboundary ExDAs. As
important examples, we consider the $E_{n(n)}$ EDA for $n\leq 8$ and study
various aspects, both in terms of M-theory and type IIB theory.
