Strong integrability of λ-deformed models

We study the notion of strong integrability for classically integrable λ-deformed CFTs and coset CFTs. To achieve this goal we employ the Poisson brackets of the spatial Lax matrix which we prove that it assumes the Maillet r/s-matrix algebra. As a consequence the system in question are integrable in the strong sense. Furthermore, we show that the derived Maillet r/s-matrix algebras can be realized in terms of twist functions, at the poles of which we recover the underlying symmetry algebras.