Martin Schlichenmaier: Krichever-Novikov type algebras - an overview

The Virasoro algebra is one of the most important infinite dimensional Lie algebras. It appears in CFT, integrable systems, etc. One of its realizations is the (centrally extended) algebra of meromorphic vector fields on the Riemann sphere having only poles at 0 and infinity. Krichever-Novikov type algebras are generalisations to higher genus Riemann surfaces and even for more than two points where poles are allowed. The graded structure of the Virasoro algebra is replaced by a weaker concept, an almost-grading - which in most cases still is enough to construct interesting representations. These algebras play e.g. a role in a global operator approach to CFT, deformation theory, moduli spaces, and so on. In the talk I will review some of the constructions of the algebras their central extensions and representations.