Imaginary roots of a Kac-Moody Lie algebra whose reflections preserve root multiplicities
type: Item
instance of: scholarly article
title: Imaginary roots of a Kac-Moody Lie algebra whose reflections preserve root multiplicities
zbMATH Open document ID: 0795.17031
published in: Journal of Algebra
publication date: 1994-09-25T00:00:00Z
review text: In contrast with finite dimensional semisimple Lie algebras, the infinite dimensional Kac-Moody Lie algebras possess some roots which are not conjugate to the simple roots under the associated Weyl group. These are the so-called imaginary roots. An imaginary root \(\alpha\) is said to be special if the corresponding reflection \(r_ \alpha\) preserves the root lattice, as well as the sets of real and imaginary roots. These special imaginary roots play an interesting role in the study of generalized spherical buildings. In this paper, the author has provided a complete classification of special imaginary roots for symmetrizable Kac-Moody Lie algebras.
Mathematics Subject Classification ID: 17B67
zbMATH DE Number: 218579
zbMATH Keywords: Coxeter group
zbMATH Keywords: infinite dimensional Kac-Moody Lie algebras
zbMATH Keywords: special imaginary roots
zbMATH Keywords: generalized spherical buildings
zbMATH Keywords: symmetrizable Kac-Moody Lie algebras
author: Curtis D. Bennett
reviewed by: Kailash C. Misra
MaRDI profile type: Publication
full work available at URL: jabr.1993.1133
OpenAlex ID: W2038114624
Wikidata QID: Q115396301
DOI: 10.1006/JABR.1993.1133
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description: scientific article; zbMATH DE number 218579