Journal of Geometry and Symmetry in Physics

Deformations of the Virasoro Algebra of Krichever-Novikov Type

Martin Schlichenmaier

Full-text: Open access

Abstract

It is the general impression that deformation problems are always governed by cohomology spaces. In this contribution we consider the deformation of Lie algebras. There this close connection is true for finite-dimensional algebras, but fails for infinite dimensional ones. We construct geometric families of infinite dimensional Lie algebras over the moduli space of complex one-dimensional tori with marked points. These algebras are algebras of Krichever-Novikov type which consist of meromorphic vector fields of certain type over the tori. The families are non-trivial deformations of the (infinite dimensional) Witt algebra, and the Virasoro algebra respectively, despite the fact that the cohomology space associated to the deformation problem of the Witt algebra vanishes, and hence the algebra is formally rigid. A similar construction works for current algebras. The presented results are jointly obtained with Alice Fialowski.

Article information

Source
J. Geom. Symmetry Phys., Volume 5 (2006), 95-105.

Dates
First available in Project Euclid: 20 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.jgsp/1495245707

Digital Object Identifier
doi:10.7546/jgsp-5-2006-95-105

Mathematical Reviews number (MathSciNet)
MR2269883

Zentralblatt MATH identifier
1196.17023

Citation

Schlichenmaier, Martin. Deformations of the Virasoro Algebra of Krichever-Novikov Type. J. Geom. Symmetry Phys. 5 (2006), 95--105. doi:10.7546/jgsp-5-2006-95-105. https://projecteuclid.org/euclid.jgsp/1495245707


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