Dressing cosets revisited

We present an alternative algebraic derivation of the dual pair of nonlinear $\sigma$-models based on the ‘dressing cosets’ extension of the Poisson-Lie $T$-duality \cite{KS1}. Then we generalize the result to dual pairs of Lagrangians not considered in \cite{KS1}. Our generalization turns out to incorporate the dualisable models constructed by Sfetsos in \cite{Sfet1}.