Geodesic
On the Killing form on Lie algebras
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2021), pp. 48-68.

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Finite-dimensional Lie algebras, whose Killing form is trivial, are studied. The main properties of the form Killing are specified, a series of examples of Lie algebras with trivial or non-trivial Killing form are given. It is given a classification of Lie algebras of dimension $\le 5$ with trivial Killing form. Some results are found about the space of all Lie algebras with the trivial Killing form.
Keywords: Lie algebra, Killing form, space of Lie algebras. 
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V. V. Gorbatsevich. On the Killing form on Lie algebras. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2021), pp. 48-68. http://geodesic.mathdoc.fr/item/IVM_2021_4_a3/

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