A structure theory of Freudenthal-Kantor triple systems
type: Item
instance of: scholarly article
title: A structure theory of Freudenthal-Kantor triple systems
zbMATH Open document ID: 0624.17002
DOI: 10.1016/0021-8693(87)90038-X
author: Noriaki Kamiya
published in: Journal of Algebra
publication date: 1987-01-01T00:00:00Z
review text: The notion of the Freudenthal-Kantor triple system (F-K triple system) was first introduced by K. Yamaguti as an algebraic system which is a generalization of the algebraic system due to Freudenthal and a modification of that system by Kantor. In this article the author defines the notion of the radical of an F-K triple system and using this, shows that a semisimple F-K triple system is decomposed into a direct sum of simple ideals. The structure groups and algebras of F-K triple systems are also defined and characterized.
Mathematics Subject Classification ID: 17A40
Mathematics Subject Classification ID: 17A65
Mathematics Subject Classification ID: 17C10
Mathematics Subject Classification ID: 17B25
zbMATH DE Number: 4012844
zbMATH Keywords: Freudenthal-Kantor triple system
zbMATH Keywords: radical
zbMATH Keywords: structure groups
reviewed by: A. Fleischer
MaRDI profile type: Publication
cites work: A Construction of Lie Algebras From J-Ternary Algebras
cites work: Q5522255
cites work: A Construction of Lie Algebras from a Class of Ternary Algebras
cites work: Q5662057
cites work: Lie groups in the foundations of geometry
cites work: A Construction of Lie Algebras by Triple Systems
cites work: Q5622399
cites work: Structure groups and Lie algebras of Jordan algebras of symmetric elements of associative algebras with involution
cites work: Lie superalgebras
cites work: Q4052314
cites work: Imbedding of Jordan Algebras into Lie Algebras. I
cites work: A Structure Theory of Lie Triple Systems
cites work: Q4103716
cites work: Jordan Tripelsysteme und die Koecher-Konstruktion von Lie Algebren
cites work: Q4143481
cites work: Q4186511
cites work: On the Freudenthal's construction of exceptional Lie algebras
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description: scientific article; zbMATH DE number 4012844