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

We construct two superalgebras associated to a punctured Riemann surface. One of them is a Lie superalgebra of the Krichever–Novikov type, the other one is a Jordan superalgebra. The constructed algebras are related in several ways (algebraic, geometric, representation theoretic, etc.). In particular, the Lie superalgebra is the algebra of derivations of the Jordan superalgebra.