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. 
@article{IVM_2021_4_a3,
     author = {V. V. Gorbatsevich},
     title = {On the {Killing} form on {Lie} algebras},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {48--68},
     publisher = {mathdoc},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_4_a3/}
}
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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/