Double loop algebras and elliptic root systems
type: Item
instance of: scholarly article
title: Double loop algebras and elliptic root systems
zbMATH Open document ID: 1365.14051
author: Kenji Iohara
author: Hiroshi Yamada
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2017-04-13T00:00:00Z
review text: An elliptic root system is a root system defined on a real vector space with positive semi-definite bilinear form whose radical is of dimension two. The paper under review explains the algebraic structure of 2-toroidal Lie algebras in terms of the corresponding elliptic root systems and elliptic Weyl groups. The paper also shows that all these objects can be naturally constructed in terms of the space of \(\overline{\partial}\)-connections on a topologically trivial principal \(G\)-bundles over an elliptic curve, where \(G\) is the corresponding double loop group.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 14J17
Mathematics Subject Classification ID: 17B65
Mathematics Subject Classification ID: 14K25
Mathematics Subject Classification ID: 22E65
zbMATH DE Number: 6705705
zbMATH Keywords: root system
zbMATH Keywords: Lie algebra
zbMATH Keywords: invariant
zbMATH Keywords: action
zbMATH Keywords: bundle
zbMATH Keywords: central extension
MaRDI profile type: Publication
full work available at URL: s10231-016-0594-3
OpenAlex ID: W2486547738
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DOI: 10.1007/S10231-016-0594-3
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description: scientific article; zbMATH DE number 6705705