Finite-dimensional Lie algebras with trivial Killing form are studied. The main properties of the Killing form are specified, a series of examples of Lie algebras with trivial or non-trivial Killing form are given. A classification of Lie algebras of dimension \(\le 5\) with trivial Killing form is given. Some results are found about the space of all Lie algebras with trivial Killing form.

中文翻译：

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关于李代数的杀死形式

研究了平凡的Killing形式的有限维Lie代数。给出了Killing形式的主要性质，给出了平凡或非平凡Killing形式的Lie代数的一系列例子。给出了维数为（\ le 5 \）的李代数的平凡Killing形式的分类。发现了所有具有平凡Killing形式的Lie代数的空间的一些结果。