Abstract

The aim of this work is to explicitly compute the semi-invariants of low-dimensional Lie algebras by reducing the amount of work, i.e., we can prove that almost every irreducible Lie algebra $\mathfrak{g},$ of dimension less than or equal to 5, satisfies the following: It is either a contact Lie algebra or there exists a torus $T\subset \text{Der}(\mathfrak{g})$ such that $T\hspace{0.17em}⋉\mathfrak{g}$ is a contact Lie algebra. Therefore, the semi-invariants found by using the contact structure are the same found by using the Frobenius structure.

中文翻译：

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低维李代数的半不变量

摘要

这项工作的目的是通过减少工作量来显式计算低维李代数的半不变量，即，我们可以证明几乎每个不可约李代数 $\mathfrak{G}，$ 小于或等于5的维，满足以下条件：它是接触李代数或存在环面 $Ť\subset \text{er}（\mathfrak{G}）$ 这样 $Ť\hspace{0.17em}⋉\mathfrak{G}$是接触李代数。因此，使用接触结构发现的半不变量与使用Frobenius结构发现的相同。