  We construct multi-brace cotensor Hopf algebras with bosonizations of quantum
multi-brace algebras as examples. Quantum quasi-symmetric algebras are then
obtained by taking particular initial data; this allows us to realize the whole
quantum group associated to a symmetrizable Kac-Moody Lie algebra as a quantum
quasi-symmetric algebra and all highest weight irreducible representations can
be constructed using this machinery. It also provides a systematic way to
construct simple modules over the quantum double of a quantum group.
