不可解Lie代数完备的等价条件

The Condition of Equivalence for the Perfect Non-solvable Lie Algebras

目的是给出特征零域上的有限维不可解L ie代数L完备的等价条件.主要是讨论L的所有导子都是内导子的充要条件.根据L的L ev i分解式(即L分解成它的根基R和另一个半单子代数S的空间直和),先在一定条件下将根基R上的导子扩充为L上的导子,给出了L完备的一个必要条件,然后又将L上的导子诱导到半单子代数S上,利用半单子代数S的完备性,证明了上述必要条件也是L完备的充分条件.

Discussed the condition of ecluivalence on which all the derivatives of L are inner. L denote the finite dimensional non-solvable Lie algebras over a field of characteristic zero. Based on the Levi decomposition of L （i. e. the decomposition of L as the direct sum of R and S, where R,S denotes the radical and a semi-simple sub-algebra of L respectively. ）, we get a necessary condition on which L is perfect by expanding the derivatives of R on L. After we induced the derivatives of L in S, we find that the necessary condition is also sufficient because of the perfect ability of semi-simple Lie algebra S.