Zhixue Zhang
Abstract
By means of studying the direct sum of root subspaces about derivation of an n-Lie algebra and regular representations of n-Lie algebras,we show that a n-Lie algebra admitting a derivation with all characteristic roots being positive real number must be nilpotent.So we can determinate the nilpotence of n-Lie algebras by the properties of derivation.
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By means of studying the direct sum of root subspaces about derivation of an n-Lie algebra and regular representations of n-Lie algebras,we show that a n-Lie algebra admitting a derivation with all characteristic roots being positive real number must be nilpotent.So we can determinate the nilpotence of n-Lie algebras by the properties of derivation.
Key concepts: Mathematics, Lie algebra, Pure mathematics, Linear subspace, Lie conformal algebra, Adjoint representation of a Lie algebra, Graded Lie algebra, Nilpotent