Ground rings and their modules in 2D gravity with c⩽1 matter

Abstract All solvable two-dimensional quantum gravity models have non-trivial BRST cohomology with vanishing ghost number. These states from a ring and all the other states in the theory fall into modules of this ring. The relations in the ring and in the modules have a physical interpretation. The existence of these rings and modules leads to non-trivial constraints on the correlation functions and goes a long way toward solving these theories in the continuum approach.