Krichever-Novikov algebras for more than two points: Explicit generators

Abstract

For the Krichever-Novikov algebras and modules of meromorphic vector fields and forms with more than two poles on higher genus Riemann surfaces, explicit expressions of the generators are given. These are expressions in terms of theta functions and prime forms for g≥1, expressions in terms of the Weierstraß σ function for g=1 and rational expressions for g=0.