Loop groups and related affine Lie algebras
type: Item
instance of: scholarly article
title: Loop groups and related affine Lie algebras
zbMATH Open document ID: 0704.17012
author: Kiyokazu Suto
published in: Proceedings of the Japan Academy. Series A
publication date: 1989-01-01T00:00:00Z
review text: Let \(G\) be a connected, simply connected complex simple Lie group, \({\mathfrak g}\) its Lie algebra. The Lie algebra \(\tilde{\mathfrak g}\) of algebraic loops in the Lie algebra \({\mathfrak g}\) of \(G\) has a universal central extension \(\hat{\mathfrak g}\) called an affine Lie algebra. In this paper, the Lie group \(\tilde G_k\) of \(C^k\)-loops in \(G\) and the Lie algebras \(\tilde{\mathfrak g}_k\), \(\hat{\mathfrak g}_k\) are discussed. A completed version of some facts on \(\tilde G\) and \(\tilde{\mathfrak g}\) for \(\tilde G_k\) and \(\hat{\mathfrak g}_k\) is constructed.
Mathematics Subject Classification ID: 17B65
Mathematics Subject Classification ID: 22E67
zbMATH DE Number: 4154684
zbMATH Keywords: adjoint action
zbMATH Keywords: affine Weyl group
zbMATH Keywords: algebraic loops
zbMATH Keywords: central extension
zbMATH Keywords: affine Lie algebra
MaRDI profile type: Publication
full work available at URL: pjaa.65.187
OpenAlex ID: W2056688927
Wikidata QID: Q115219939
cites work: The arithmetic theory of loop groups
cites work: Structure and unitary cocycle representations of loop groups and the group of diffeomorphisms of the circle.
cites work: Infinite dimensional Lie algebras. An introduction
cites work: Q3710720
cites work: Infinite flag varieties and conjugacy theorems
cites work: Q3215137
DOI: 10.3792/PJAA.65.187
description: scientific article; zbMATH DE number 4154684