Abstract
In the paper, Lie algebras having bases of a special form (nice and beautiful bases) are considered. For nice bases, it is proved that, in a chosen nilpotent Lie algebra, their number (up to equivalence) is finite. For some Lie algebras of low dimension, it is shown that, when passing from a complex Lie algebra to its realification, the property to have a beautiful basis is lost.
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Translated from Matematicheskie Zametki, 2023, Vol. 114, pp. 203–211 https://doi.org/10.4213/mzm13741.
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Gorbatsevich, V.V. On Some Classes of Bases in Finite-Dimensional Lie Algebras. Math Notes 114, 165–171 (2023). https://doi.org/10.1134/S0001434623070180
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DOI: https://doi.org/10.1134/S0001434623070180