  Invited talk at the International Symposium on Generalized Symmetries in
Physics at the Arnold-Sommerfeld-Institute, Clausthal, Germany, July 26 -- July
29, 1993. This talk reviews results on the structure of algebras consisting of
meromorphic differential operators which are holomorphic outside a finite set
of points on compact Riemann surfaces. For each partition into two disjoint
subsets of the set of points where poles are allowed, a grading of the algebra
and of the modules of lambda - forms is introduced. With respect to this
grading the Lie structure of the algebra and of the modules are almost graded
ones. Central extensions and semi-infinite wedge representations are studied.
If one considers only differential operators of degree 1 then these algebras
are generalizations of the Virasoro algebra in genus zero, resp. of Krichever
Novikov algebras in higher genus.
