  We summarize some recent results obtained in collaboration with J. McCarthy
on the spectrum of physical states in $W_3$ gravity coupled to $c=2$ matter. We
show that the space of physical states, defined as a semi-infinite (or BRST)
cohomology of the $W_3$ algebra, carries the structure of a BV-algebra. This
BV-algebra has a quotient which is isomorphic to the BV-algebra of polyvector
fields on the base affine space of $SL(3,C)$. Details have appeared elsewhere.
[Published in the proceedings of "Gursey Memorial Conference I: Strings and
Symmetries," Istanbul, June 1994, eds. G. Aktas et al., Lect. Notes in Phys.
447, (Springer Verlag, Berlin, 1995)]
