Coupled Susy, pseudo-bosons and a deformed su(1,1) Lie algebra

In a recent paper a pair of operators a and b satisfying the equations a(dagger)a = bb(dagger) + gamma 1 and aa(dagger) = b(dagger)b + delta 1, has been considered, and their nature of ladder operators has been deduced and analyzed. Here, motivated by the spreading interest in non self-adjoint operators in quantum mechanics, we extend this situation to a set of four operators, c, d, r and s, satisfying dc = rs + delta 1 and cd = sr + delta 1, and we show that they arc also ladder operators. We show their connection with biorthogonal families of vectors and with the so-called To-pseudo bosons. Some examples are discussed.