Kazama–Suzuki models of $N=2$ superconformal field theory and Manin triples

Kazama–Suzuki coset models is an interesting class of $N=2$ supersymmetric models of conformal field theory which are used to build realistic models of superstring in 4 dimensions. We formulate Kazama–Suzuki construction of $N=2$ superconformal coset models using more general language of Manin triples and represent the corresponding $N=2$ Virasoro superalgebra currents in explicit form.