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Abstract

Poisson-Lie duality provides an algebraic extension of conventional Abelian
and non-Abelian target space dualities of string theory and has seen recent
applications in constructing quantum group deformations of holography. Here we
demonstrate a natural upgrading of Poisson-Lie to the context of M-theory using
the tools of exceptional field theory. In particular, we propose how the
underlying idea of a Drinfeld double can be generalised to an algebra we call
an exceptional Drinfeld algebra. These admit a notion of "maximally isotropic
subalgebras" and we show how to define a generalised Scherk-Schwarz truncation
on the associated group manifold to such a subalgebra. This allows us to define
a notion of Poisson-Lie U-duality. Moreover, the closure conditions of the
exceptional Drinfeld algebra define natural analogues of the cocycle and
co-Jacobi conditions arising in Drinfeld double. We show that upon making a
further coboundary restriction to the cocycle that an M-theoretic extension of
Yang-Baxter deformations arise. We remark on the application of this
construction as a solution-generating technique within supergravity.