The ring structure of Lian-Zuckerman states for $(q,p)$ minimal models coupled to gravity is shown to be ${ \cal R}={ \cal R}_0\otimes { \bf C} [w,w^{ -1}]$ where ${ \cal R}_0$ is the ring of ghost number zero operators generated by two elements and $w$ is an operator of ghost number $-1$. Some examples are discussed in detail. For these models the currents are also discussed and their algebra is shown to contain the Virasoro algebra.
Categories: hep-th