Algebraic properties of a special class of birth-death master equations

We give a complete description of a simple special class of stochastic models (birth-death master equations). Each equation of this class can be easily solved by the method suggested by supersymmetric quantum mechanics. Using the quadratic Lyapunov functional, one can transform the master equation to a Schroedinger-type equation with a self-adjoint Hamiltonian in imaginary time. Then the hidden symmetries of the Hamiltonian are investigated. The whole set of models can be decomposed to four subsets with natural algebraic classification. (author)