  We consider a nonequilibrium reaction-diffusion model on a finite one
dimensional lattice with bulk and boundary dynamics inspired by Glauber
dynamics of the Ising model. We show that the model has a rich algebraic
structure that we use to calculate its properties. In particular, we show that
the Markov dynamics for a system of a given size can be embedded in the
dynamics of systems of higher sizes. This remark leads us to devise a technique
we call the transfer matrix Ansatz that allows us to determine the steady state
distribution and correlation functions. Furthermore, we show that the disorder
variables satisfy very simple properties and we give a conjecture for the
characteristic polynomial of Markov matrices. Lastly, we compare the transfer
matrix Ansatz used here with the matrix product representation of the steady
state of one-dimensional stochastic models.
