论文标题
半主导谎言代数的不变性
Invariants of a semi-direct sum of Lie algebras
论文作者
论文摘要
我们表明，如果与Levi Factor $ s $的Lie代数的任何半主导总和$ L $，则如果与之相关的表示不具有微不足道的代表副本，则必须是完美的。结果，$ l $的所有不变功能都必须是卡西米尔运营商。当$ s = \ frak {sl}（2，\ mathbb {k}）时，$对于$ l $的所有可能维度给出了不变的数量。通过解决总体方程式系统的等效问题来替换传统的方法来确定PDE的系统，对于根部的所有维度都可以找到不变的系统，最多五个。对获得的结果进行了分析，这仅取决于某些亚代代代代数的元素，导致对谎言代数的不变性定理。
We show that any semi-direct sum $L$ of Lie algebras with Levi factor $S$ must be perfect if the representation associated with it does not possess a copy of the trivial representation. As a consequence, all invariant functions of $L$ must be Casimir operators. When $S= \frak{sl}(2,\mathbb{K}),$ the number of invariants is given for all possible dimensions of $L$. Replacing the traditional method of solving the system of determining PDEs by the equivalent problem of solving a system of total differential equations, the invariants are found for all dimensions of the radical up to five. An analysis of the results obtained is made, and this lead to a theorem on invariants of Lie algebras depending only on the elements of certain subalgebras.
