  Using the Lindblad master equation approach, we investigate the structure of
steady-state solutions of open integrable quantum lattice models, driven far
from equilibrium by incoherent particle reservoirs attached at the boundaries.
We identify a class of boundary dissipation processes which permits to derive
exact steady-state density matrices in the form of graded matrix-product
operators. All the solutions factorize in terms of vacuum analogues of Baxter's
Q-operators which are realized in terms of non-unitary representations of
certain finite dimensional subalgebras of graded Yangians. We present a
unifying framework which allows to solve fermionic models and naturally
incorporates higher-rank symmetries. This enables to explain underlying
algebraic content behind most of the previously-found solutions.
