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.

中文翻译：

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有限维李代数中的几类基

摘要

在本文中，考虑了具有特殊形式的基（漂亮且美丽的基）的李代数。对于好基，证明了在选定的幂零李代数中，它们的数量（直到等价）是有限的。对于一些低维的李代数，结果表明，当从复杂的李代数过渡到其实现时，拥有美丽基础的性质就消失了。