We give the general structure of complex (resp., real) $G$-gradedcontractions of Lie algebras where $G$ is an arbitrary finite Abeliangroup. For this purpose, we introduce a number of concepts, such aspseudobasis, higher-order identities, and sign invariants. Wecharacterize the equivalence classes of $G$-graded contractions byshowing that our set of invariants (support, higher-order identities,and sign invariants) is complete, which yields a classification.
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机译：我们给出Lie代数的复数（分别为实数）$ G $级的压缩的一般结构，其中$ G $是任意有限的阿贝尔群。为此，我们介绍了许多概念，例如假单胞菌，高阶恒等式和符号不变式。通过证明我们的一组不变式（支持，高阶恒等式和符号不变式）是完整的，我们得出了G $级收缩的等价类的特征。
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