Four dimensional realization of two dimensional current groups
type: Item
instance of: scholarly article
title: Four dimensional realization of two dimensional current groups
zbMATH Open document ID: 0858.22017
DOI: 10.1007/BF02108814
published in: Communications in Mathematical Physics
publication date: 1997-03-18T00:00:00Z
review text: Affine Lie groups are realized as quotients of central extensions of the current groups over Riemann surfaces. This is achieved by means of the Leray residue theory which replaces de Rham cohomology in the classical Wess-Zumino-Novikov-Witten (WZNW) construction for affine Lie groups. A review of the results on central extension of current algebras and current groups in two dimensions is first given. Then, these results are generalized to currents over Riemann surfaces with punctures. The four dimensional realization of two dimensional current groups is obtained by using Leray theory. The case of a punctured sphere is considered as an illustrative example.
Mathematics Subject Classification ID: 22E65
Mathematics Subject Classification ID: 81R10
zbMATH DE Number: 934331
zbMATH Keywords: Wess-Zumino-Novikov-Witten construction
zbMATH Keywords: Lie groups
zbMATH Keywords: central extensions
zbMATH Keywords: Riemann surfaces
zbMATH Keywords: Leray residue theory
zbMATH Keywords: current groups
author: Igor B. Frenkel
author: Boris Khesin
reviewed by: Gheorghe Zet
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02108814
OpenAlex ID: W2062224326
description: scientific article; zbMATH DE number 934331