In this paper we translate the necessary and sufficient conditions of Tanaka’s theorem on the finiteness of effective prolongations of a fundamental graded Lie algebras into computationally effective criteria, involving the rank of some matrices that can be explicitly constructed. Our results would apply to geometries, which are defined by assigning a structure algebra on the contact distribution.

中文翻译：

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$${{\,\mathrm{{\mathfrak {L}}}\,}}$$L-分级李代数的延展

在本文中，我们将关于基本分级李代数的有效延拓的有限性的 Tanaka 定理的充要条件转化为计算上有效的标准，其中涉及一些可以明确构造的矩阵的秩。我们的结果适用于几何体，几何体是通过在接触分布上分配结构代数来定义的。