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A generalization of the Yang-Baxter algebra is found in quantizing themonodromy matrix of two (m)KdV equations discretized on a space lattice. Thisbraided Yang-Baxter equation still ensures that the transfer matrix generatesoperators in involution which form the Cartan sub-algebra of the braidedquantum group. Representations diagonalizing these operators are describedthrough relying on an easy generalization of Algebraic Bethe Ansatz techniques.The conjecture that this monodromy matrix algebra leads, {\it in the cylindercontinuum limit}, to a Perturbed Minimal Conformal Field Theory description isanalysed and supported.Comment: Latex file, 46 page

A braided Yang–Baxter algebra in a theory of two coupled lattice quantum KdV: algebraic properties and ABA representations