讨论李三系T的导子的有关内容,并且给出了完备李三系的定义,进而得到完备李三系的分解定理,即完备李三系可以分解成理想的直和,且李三系完备当且仅当理想完备,并且由标准嵌入李代数的完备性可以证得李三系的完备性,以及其它一些重要性质.
The author further discuss the derivations of a Lie triple system T over a field F, and define com-plete Lie triple system and show some properties for complete T.
[1] Meng D J, ZHU L S, JIANG C P. CompleteLie algebras [M]. 北京:科学出版社 2001.
[2] LISTER W G. A structure theory of Lie triple system [J]. Transactions of the American Mathematical Society 1952, 72.
[3] MEYBERG K. Lectures on Algebras and Triple Systems [M]. Charlottesville:University of Virginia 1972.
[4] Humphrey J E. I ntroduction to Lie algebra and representation theory [M]. Heidelberg:SpringerVerlag 1972.
[5] HOPKINS N C. Nilpotent ideal in Lie and anti-Lie triple system [J]. Journal of Algebra 1995, 178.
