论文标题
有限维谎言代数的光谱不变
Spectral invariants for finite dimensional Lie algebras
论文作者
论文摘要
对于lie代数$ {\ Mathcal l} $，带有$ \ {x_1，x_2，x_2，\ cdots，x_n \} $，其关联的特征性多项式$ q _ {\ Mathcal l} \ Mathcal l}（z）$是线性铅笔$ z_0i $ z_0i+Z____________________ cd cd cd cd cd cd cd cd x x +z_n \ text {ad} x_n。$本文表明，$ q _ {\ Mathcal l} $在自动形态组$ \ text {aut}（{\ mathcal l}）下是不变的。$ $ Q _ {\ Mathcal l} $的零品种和分解$ q cal l}在这种情况下，$ {\ Mathcal l} $是可解决的$ q _ {\ Mathcal L} $是线性因素的产物。这一事实引起了光谱矩阵的定义，而庞加莱多项式用于可溶解的谎言代数。将申请给出$ 1 $维的nilpotent Lie代数的扩展。
For a Lie algebra ${\mathcal L}$ with basis $\{x_1,x_2,\cdots,x_n\}$, its associated characteristic polynomial $Q_{\mathcal L}(z)$ is the determinant of the linear pencil $z_0I+z_1\text{ad} x_1+\cdots +z_n\text{ad} x_n.$ This paper shows that $Q_{\mathcal L}$ is invariant under the automorphism group $\text{Aut}({\mathcal L}).$ The zero variety and factorization of $Q_{\mathcal L}$ reflect the structure of ${\mathcal L}$. In the case ${\mathcal L}$ is solvable $Q_{\mathcal L}$ is known to be a product of linear factors. This fact gives rise to the definition of spectral matrix and the Poincaré polynomial for solvable Lie algebras. Application is given to $1$-dimensional extensions of nilpotent Lie algebras.
