Deformation of current algebras in \(3+1\) dimensions
type: Item
instance of: scholarly article
title: Deformation of current algebras in \(3+1\) dimensions
zbMATH Open document ID: 0728.17014
DOI: 10.1007/BF00401651
author: Jouko Mickelsson
author: S. G. Rajeev
published in: Letters in Mathematical Physics
publication date: 1991-01-01T00:00:00Z
review text: In a previous paper [Commun. Math. Phys. 116, 365-400 (1988; Zbl 0648.22013)], the authors attempted to construct a unitary representation of the group XG of maps from a compact 3-manifold X into a compact Lie group G by embedding XG into an infinite-dimensional general linear group \(GL_ 2\). However, it turned out that the representations constructed were not, in fact, unitary. In the present paper, the authors construct a 3-parameter deformation of (the universal central extension of) the Lie algebra of \(GL_ 2\), together with representations which are unitary for certain values of the deformation parameter.
reviewed by: Andrew N. Pressley
Mathematics Subject Classification ID: 17B65
Mathematics Subject Classification ID: 22E65
Mathematics Subject Classification ID: 81R10
zbMATH DE Number: 4202534
zbMATH Keywords: highest-weight nonunitary representations
zbMATH Keywords: current algebras
zbMATH Keywords: deformation
MaRDI profile type: Publication
cites work: Current algebras in \(d+1\)-dimensions and determinant bundles over infinite-dimensional Grassmannians
cites work: Q3999168
cites work: On the Mickelsson-Faddeev extension and unitary representations
cites work: Q3857325
cites work: Quasi-free 'second quantization'
cites work: Q3754832
full work available at URL: https://doi.org/10.1007/bf00401651
OpenAlex ID: W1983414627
description: scientific article; zbMATH DE number 4202534