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On the Killing form on Lie Algebras

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Abstract

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.

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Authors and Affiliations

  1. Moscow Aviation Institute, 4 Volokolamsk hwy., 125993, Moscow, Russia

    V. V. Gorbatsevich

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  1. V. V. Gorbatsevich
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Correspondence to V. V. Gorbatsevich.

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Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 4, pp. 48–68.

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Gorbatsevich, V.V. On the Killing form on Lie Algebras. Russ Math. 65, 44–60 (2021). https://doi.org/10.3103/S1066369X21040046

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  • DOI: https://doi.org/10.3103/S1066369X21040046

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