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| 摘要: |
| 本文研究了带有相关0根空间的任意分裂的δ-Jordan李三系的结构.利用这种三系的根连通，得到了带有对称根系的分裂的δ-Jordan李三系T可以表示成T=U+Σ[α]∈Λ1/~ I[α]，其中U是0根空间T0的子空间，任意I[α]为T的理想，并且满足当[α]≠[β]时，[I[α]，T，I[β]]=0. |
| 关键词: 分裂的δ-Jordan李三系 李三系 δ-Jordan李代数 根系 根空间 |
| DOI： |
| 分类号:O152.5 |
| 基金项目:Supported by National Natural Science Foundation of China (11801121); NSF of Heilongjiang Province (QC2018006) and the Fundamental Research Fundation for Universities of Heilongjiang Province (LGYC2018JC002). |
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| ON THE STRUCTURE OF SPLIT δ-JORDAN LIE TRIPLE SYSTEMS |
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CAO Yan
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| Abstract: |
| The aim of this article is to study the structure of arbitrary split δ-Jordan Lie triple systems by focussing on those with a coherent 0-root space. By developing techniques of connections of roots for this kind of triple system T, we show that such an arbitrary δ-JLTS with a symmetric root system is of the form T=U+Σ[α]∈Λ1/~ I[α] with U a subspace of the 0-root space T0 and any I[α] a well described ideal of T, satisfying [I[α], T, I[β]] = 0 if [α]≠[β]. |
| Key words: split δ-Jordan Lie triple system Lie triple system δ-Jordan Lie algebra root system root space |
