| 李军波,法焕霞.一类单完备李代数[J].数学年刊A辑,2009,30(3):401~410 |
| 一类单完备李代数 |
| A Class of Simple Complete Lie Algebras |
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| DOI： |
| 中文关键词: 导子代数 内导子 单完备李代数 |
| 英文关键词:Derivation algebra, Inner derivations, Simple complete Lie algebras |
| 基金项目:国家自然科学基金(No.10671027;No.10825101)资助的项目 |
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| 中文摘要: |
| 确定了代数Va,b.c的导子代数,其中Va.b.c是由非交换代数Ca,b,c[X±1,Y±1,Z±1]的所有内导子所张成的李代数,证明了导子代数数Va.b,c是由所有内导子和3个外导子D1,0,0,DO,1,0,D0,0,1张成的,同时还给出了一类无限维的单完备李代数. |
| 英文摘要: |
| The derivation algebra of the algebra
$V_{a,b,c}$ is determined in this paper, where $V_{a,b,c}$ denotes
the Lie algebra of inner derivations of the algebra
$\C_{a,b,c}[X^{\pm1},Y^{\pm1},Z^{\pm1}]$. It is proved that the Lie
algebra of derivations of $V_{a,b,c}$ is spanned by the inner
derivations and three outer derivations $D_{1,0,0},D_{0,1,0}$ and
$D_{0,0,1}$. As a result, an infinite simple complete Lie
algebra is presented. |
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