幂零可解三角李代数的不变量
Invariants of the nilpotent and solvable triangular Lie algebras
摘要：
计算了两类李代数的余伴随表示的不变量。第一类由幂零李代数$T(M)$组成，同构于上三角$M\times M$矩阵的代数。证明了李代数$T(M)$具有$[M/2]$函数独立不变量.它们都可以被选择为多项式，并且它们被显式地呈现。第二类由可解李代数$L(M,f)$组成，其中$T(M)$为其零根，$f$具有额外的线性零无关元。给出了关于$L(M,f)$的不变量的一些一般性结果，并详细讨论了M = 4的情形对所有的$f$和$f=1$，或$f=M-1$对所有的$M$.
英文摘要：
Invariants of the coadjoint representation of two classes of Lie algebras are calculated. The first class consists of the nilpotent Lie algebras $T(M)$, isomorphic to the algebras of upper triangular $M\times M$ matrices. The Lie algebra $T(M)$ is shown to have $[M/2]$ functionally independent invariants. They can all be chosen to be polynomials and they are presented explicitly. The second class consists of the solvable Lie algebras $L(M,f)$ with $T(M)$ as their nilradical and $f$ additional linearly nilindependent elements. Some general results on the invariants of $L(M,f)$ are given and the cases M=4 for all $f$ and $f=1$, or $f=M-1$ for all $M$ are treated in detail.
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