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Abstract
In this article, we introduce the notion of system of quotients of Lie triple systems and investigate some properties which can be lifted from a Lie triple system to its systems of quotients. We relate the notion of Lie triple system of Martindale-like quotients with respect to a filter of ideals and the notion of system of quotients, and prove that the system of quotients of a Lie triple system is equivalent to the algebra of quotients of a Lie algebra in some sense, and these allow us to construct the maximal system of quotients for nondegenerate Lie triple systems.
Mathematics Subject Classification (2010):
ACKNOWLEDGMENTS
The authors would like to thank the referee for valuable comments and suggestions on this article.
The work was supported by NNSF of China (No. 11171055, No. 11226054), NSF of Jilin Province (No. 201115006), Scientific Research Foundation for Returned Scholars Ministry of Education of China, and the Fundamental Research Funds for the Central Universities (No. 12SSXT139).
Notes
Communicated by A. Elduque.