Involutive Lie algebras graded by finite root systems and compact forms of IM algebras
type: Item
instance of: scholarly article
title: Involutive Lie algebras graded by finite root systems and compact forms of IM algebras
zbMATH Open document ID: 0884.17012
DOI: 10.1007/PL00004280
author: Yun Gao
published in: Mathematische Zeitschrift
publication date: 1997-07-03T00:00:00Z
full work available at URL: https://eudml.org/doc/174944
review text: An intersection-matrix (IM) Lie algebra is defined through an analogue of the Chevalley basis of a simple Lie algebra associated with an intersection matrix \(A= (a_{ij})_{n\times n}\) \((a_{ii}=2\), \(a_{ij}<0 \iff a_{ji}<0\), \(0<a_{ij} \iff 0<a_{ji}\)). For any IM algebra, there exists an analogue of the Chevalley involution. The author shows that the fixed-point subalgebra of this involution is isomorphic to a certain Steinberg unitary Lie algebra which was introduced by \textit{B. N. Allison} and \textit{J. R. Faulkner} [J. Algebra 161, 1-19 (1993; Zbl 0812.17002)]. Moreover, the author introduces an analogue of the elementary unitary Lie algebra of other types and studies involutive Lie algebras graded by finite root systems.
Mathematics Subject Classification ID: 17B67
zbMATH DE Number: 1028276
zbMATH Keywords: intersection-matrix
zbMATH Keywords: IM algebra
zbMATH Keywords: Chevalley involution
zbMATH Keywords: Steinberg unitary Lie algebra
zbMATH Keywords: involutive Lie algebras
reviewed by: Xiaoping Xu
MaRDI profile type: Publication
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OpenAlex ID: W1981755868
description: scientific article; zbMATH DE number 1028276