$N$-point Virasoro algebras are multi-point Krichever--Novikov type algebras

Abstract

We show how the recently again discussed $N$-point Witt, Virasoro, and affine Lie algebras are genus zero examples of the multi-point versions of Krichever--Novikov type algebras as introduced and studied by Schlichenmaier. Using this more general point of view, useful structural insights and an easier access to calculations can be obtained. The concept of almost-grading will yield information about triangular decompositions which are of importance in the theory of representations. As examples the algebra of functions, vector fields, differential operators, current algebras, affine Lie algebras, Lie superalgebras and their central extensions are studied. Very detailed calculations for the three-point case are given.

arXiv comment46 pages

References in corpus (7)

• Reduction Groups and Automorphic Lie Algebras
• The Wess-Zumino-Witten-Novikov theory, Knizhnik-Zamolodchikov equations, and Krichever-Novikov algebras, I
• Degenerations of Generalized Krichever Novikov algebras on Tori
• Global Geometric Deformations of the Virasoro algebra, current and affine algebras by Krichever-Novikov type algebra
• Extensions of superalgebras of Krichever-Novikov type
• Towards Vertex Algebras of Krichever-Novikov Type, Part I
• Determination of the 2- cocycles for the three point Witt algebra

Cited by in corpus (2)

• The 3-point Virasoro algebra and its action on a Fock space
• Module structure of the center of the universal central extension of a genus zero Krichever-Novikov algebra