The Frattini Subsystem of a Lie Triple System

As an analogue of the Frattini algebra of a Lie algebra, the Frattini subsystem of a Lie triple system is defined and some elementary properties are investigated. Some further results concerning Frattini subsystems for nilpotent Lie triple systems and solvable Lie triple systems are obtained. Moreov...

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Bibliographic Details
Published in:Communications in algebra 2009-10, Vol.37 (10), p.3750-3759
Main Authors: Zhang, Zhixue, Chen, Liangyun, Liu, Wenli, Bai, Ximei
Format: Article
Language:English
Subjects:
Frattini subsystem
Jacobson radical
Lie triple systems
Φ-Free
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Summary:As an analogue of the Frattini algebra of a Lie algebra, the Frattini subsystem of a Lie triple system is defined and some elementary properties are investigated. Some further results concerning Frattini subsystems for nilpotent Lie triple systems and solvable Lie triple systems are obtained. Moreover, some necessary and sufficient conditions for a Lie triple system to be Φ-free are given.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927870802502936