Differential Operator Algebras on compact Riemann Surfaces

Abstract

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.

11 pages, AmsTeX 2.1 and psbox macros

References in corpus (1)

• Degenerations of Generalized Krichever Novikov algebras on Tori

Cited by in corpus (6)

• The Wess-Zumino-Witten-Novikov theory, Knizhnik-Zamolodchikov equations, and Krichever-Novikov algebras, I
• Global Geometric Deformations of the Virasoro algebra, current and affine algebras by Krichever-Novikov type algebra
• Boson-fermion correspondence of type D-A and multi-local Virasoro representations on the Fock space $F^{\otimes \frac{1}{2}}$
• Sugawara Construction and Casimir Operators for Krichever-Novikov Algebras
• Sugawara Construction for Higher Genus Riemann Surfaces
• Higher Genus Affine Lie Algebras of Krichever -- Novikov Type