  T-duality of string theory can be extended to the Poisson-Lie T-duality when
the target space has a generalized isometry group given by a Drinfel'd double.
In M-theory, T-duality is understood as a subgroup of U-duality, but the
non-Abelian extension of U-duality is still a mystery. In this paper, we study
membrane theory on a curved background with a generalized isometry group given
by the $\mathcal{E}_n$ algebra. This provides a natural setup to study
non-Abelian U-duality because the $\mathcal{E}_n$ algebra has been proposed as
a U-duality extension of the Drinfel'd double. We show that the standard
treatment of Abelian U-duality can be extended to the non-Abelian setup.
However, a famous issue in Abelian U-duality still exists in the non-Abelian
extension.
