3-graded decompositions of exceptional Lie algebras \(\mathfrak g\) and group realizations of \(\mathfrak g_{ev},\mathfrak g_0\) and \(\mathfrak g_{ed}\). I: \(G=G_2,F_4,E_6\)
type: Item
instance of: scholarly article
title: 3-graded decompositions of exceptional Lie algebras \(\mathfrak g\) and group realizations of \(\mathfrak g_{ev},\mathfrak g_0\) and \(\mathfrak g_{ed}\). I: \(G=G_2,F_4,E_6\)
zbMATH Open document ID: 1042.17004
author: Ichiro Yokota
published in: Journal of Mathematics of Kyoto University
publication date: 2001-01-01T00:00:00Z
review text: Let \(\mathfrak g\) be a simple Lie algebra such that \(\mathfrak g = \sum_{k=-3}^3 \mathfrak g_k\); \([\mathfrak g_i; \mathfrak g_j] \subset \mathfrak g_{i+j}\). This is known as a 3-graded decomposition of \(\mathfrak g\). Let \(\mathfrak g_{ev} = \mathfrak g_{-2} \oplus \mathfrak g_0 \oplus \mathfrak g_2\) and \(\mathfrak g_{ed} = \mathfrak g_{-3} \oplus \mathfrak g_0 \oplus \mathfrak g_3\). The author reports that M. Hara has classified the 3-graded decompositions of simple Lie algebras \(\mathfrak g\) and determined the types of subalgebras \(\mathfrak g_{ev}; \mathfrak g_0\); and \(\mathfrak g_{ed}\). He gives a table listing Hara's results for \(\mathfrak g\) of types \(G_2; F_4\); and \(E_6\). He then determines the subgroups \(G_{ev}; G_0; G_{ed}\) of the exceptional Lie groups \(G\) of types \(G_2; F_4\); and \(E_6\) corresponding to the subalgebras \(\mathfrak g_{ev}; \mathfrak g_0; \mathfrak g_{ed}\) of \(\mathfrak G = \text{Lie} ~G\).
Mathematics Subject Classification ID: 17B25
Mathematics Subject Classification ID: 17B70
Mathematics Subject Classification ID: 22E60
zbMATH DE Number: 1803228
Wikidata QID: Q115240448
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250517613
OpenAlex ID: W4244866533
DOI: 10.1215/KJM/1250517613
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description: scientific article; zbMATH DE number 1803228