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    • 刘文丽,张知学.二次李三系的分解定理[J].数学年刊A辑,2011,32(4):385~392
    二次李三系的分解定理
    The Decomposition Theorems of Quadratic Lie Triple Systems
      
    DOI：
    中文关键词:  二次李三系  f-不可分解理想  非退化不变对称双线性型  正交直和  f-迷向的  
    英文关键词:Quadratic Lie triple system  f-Indecomposable ideal  Nondegenerate invariant symmetric bilinear form  Orthogonal direct sum  f-Isotropic  
    基金项目:河北省自然科学基金(No08M005,NoA2007000138)资助的项目
    Author NameAffiliationE-mail
    LIU Wenli College of Mathematics and Computer Science,Hebei University,Baoding 071002,Hebei,China. liuwl hb@yahoo.com.cn 
    ZHANG Zhixue College of Mathematics and Computer Science,Hebei University,Baoding 071002,Hebei,China. zzx hb@yahoo.com.cn 
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    中文摘要:
          有限维李三系称为二次的, 如果它容许一个非退化的不变对称双线性型. 无论是李三系分解为不可分解理想的直和, 还是二次李三系分解为不可分解非退化理想的正交直和, 证明了这两类分解在同构意义下都是唯一的.
    英文摘要:
          A finite dimensional Lie triple system is called quadratic if it possesses a nondegenerate invariant symmetric bilinear form. It is proved that either the decomposition of a Lie triple system into a direct sum of indecomposable ideals or the decomposition of a quadratic Lie triple system into an orthogonal direct sum of indecomposable nondegenerate ideals, is unique up to an isomorphism.
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