English

Differential Operator Algebras on compact Riemann Surfaces

High Energy Physics - Theory 2009-09-25 v1 alg-geom Quantum Algebra

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.

Keywords

Cite

@article{arxiv.hep-th/9311036,
  title  = {Differential Operator Algebras on compact Riemann Surfaces},
  author = {Martin Schlichenmaier},
  journal= {arXiv preprint arXiv:hep-th/9311036},
  year   = {2009}
}

Comments

11 pages, AmsTeX 2.1 and psbox macros

R2 v1 2026-07-22T15:47:55.975Z