Bosonic realizations of higher-level toroidal Lie algebras
type: Item
instance of: scholarly article
title: Bosonic realizations of higher-level toroidal Lie algebras
zbMATH Open document ID: 1112.17022
author: Naihuan Jing
author: Kailash C. Misra
author: Shaobin Tan
published in: Pacific Journal of Mathematics
publication date: 2006-03-10T00:00:00Z
review text: Toroidal Lie algebras are natural generalizations of the affine Kac-Moody Lie algebras, where the ring of Laurant polynomials in one variable (affine case) is now replaced with the ring of Laurent polynomials in several variables (toroidal case). The variable should be viewed as the coordinates of the torus, which explains the name ``toroidal''. It is known that every affine Lie algebra extends to a semidirect product with the \((c=0)\) Virasoro algebra. Similarly, a toroidal algebra admits a central extension with the space of Kähler differentials modulo exact terms. In the paper under review the authors construct a bosonic representation of the 2-toroidal algebra associated with the Lie algebra \(sl_2\), with rather mild constraints on the level. It is fair to say that this construction is a toroidal counterpart of the Wakimoto's realization for \(\hat{sl}_2\). The main results are Theorem 3.5 (the actual realization), Theorem 4.2 (module structure) and Theorem 4.3 (explicit computation of the characters).
reviewed by: A. Milas
Mathematics Subject Classification ID: 17B65
Mathematics Subject Classification ID: 17B69
zbMATH DE Number: 5011485
zbMATH Keywords: toroidal Lie algebras
zbMATH Keywords: affine Lie algebras
zbMATH Keywords: vertex operators
MaRDI profile type: Publication
full work available at URL: pjm.2005.219.285
OpenAlex ID: W1977411873
DOI: 10.2140/PJM.2005.219.285
description: scientific article; zbMATH DE number 5011485