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Abstract
In this paper, we consider the decomposition of a quadratic Lie algebra and the main result is that the decomposition of a quadratic Lie algebra into irreducible nondegenerate ideals is unique up to an isometry (Theorem 3.1). As a corollary, we obtain the uniqueness of the decomposition of an arbitrary Lie algebra into indecomposable ideals up to an isomorphism (Corollary 3.5.4).
ACKNOWLEDGMENTS
This work is supported by (19971044, 19901015) the National Science Foundation of China, (97005511) the Doctoral Programme Foundation of Institution of Higher Education and the Foundation of Jiangsu Educational Committee.