Xianjun Cui
Abstract
In this paper,complete n-Lie algebras were introduced and examples of complete n-Lie algebras were presented firstly,and then the examples illustrate that semi-simple n-Lie algebra is not necessarily complete n-Lie algebra.Finally,the decompositions of complete n-Lie were obtained using the properties of derivations of n-Lie algebras.
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In this paper,complete n-Lie algebras were introduced and examples of complete n-Lie algebras were presented firstly,and then the examples illustrate that semi-simple n-Lie algebra is not necessarily complete n-Lie algebra.Finally,the decompositions of complete n-Lie were obtained using the properties of derivations of n-Lie algebras.
Key concepts: Mathematics, Lie conformal algebra, Adjoint representation of a Lie algebra, Killing form, Lie algebra, Graded Lie algebra, Pure mathematics, Affine Lie algebra