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

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