Superalgebras Associated to Riemann Surfaces: Jordan Algebras of Krichever–Novikov Type

Abstract

In 1987, Krichever and Novikov [12–14] introduced a family of Lie algebras generalizing the Virasoro algebra. Given a Riemann surface of arbitrary genus, the Krichever–Novikov algebra is the algebra of meromorphic vector fields on the surface which are holomorphic outside two distinguish fixed points. This algebra admits nontrivial central extensions. The case where the Riemann surface is the sphere corresponds exactly to the Virasoro algebra. Later, this definition has been extended to the