标题： 微分算子代数在紧致黎曼曲面上 显示英文标题

标题： Differential Operator Algebras on compact Riemann Surfaces

摘要： 1993年7月26日至29日，在德国克劳斯塔尔的阿诺德-索末菲研究所举行的国际广义对称性物理研讨会上所做的邀请报告。 本次报告回顾了关于由在紧致黎曼曲面上允许极点的有限个点以外是全纯的亚纯微分算子组成的代数结构的结果。 对于允许极点的点集的两个不相交子集的划分，引入了该代数以及λ-形式模的分级。 相对于这种分级，该代数和模的李结构几乎是分级的。 研究了中心扩张和半无限楔形表示。 如果只考虑次数为1的微分算子，则这些代数在零亏格情况下是Virasoro代数的推广，在高亏格情况下是Krichever-Novikov代数的推广。 显示英文摘要

摘要： 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.