Abstract In this paper, Jordan–Kronecker invariants are calculated for all nilpotent 6- and 7-dimensional Lie algebras. We consider the Poisson bracket family, depending on the lambda parameter on a Lie coalgebra, i.e., on the linear space dual to a Lie algebra. For some space proposed in the paper, two skew-symmetric matrices are defined for all points x on this linear space. To understand the behaviour of the matrix pencil (A ? λB)(x), we consider Jordan–Kronecker invariants for this pencil and how they change with x (the latter is done for 6-dimensional Lie algebras).
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机译：摘要 计算了所有无幂6维和7维李代数的Jordan-Kronecker不变量。我们考虑泊松括号族，这取决于李代数上的 lambda 参数，即对偶于李代数的线性空间。对于本文提出的一些空间，为该线性空间上的所有点 x 定义了两个偏对称矩阵。为了理解矩阵铅笔（A ？ λB）（x）的行为，我们考虑了这支铅笔的Jordan-Kronecker不变量以及它们如何随x变化（后者是针对6维李代数完成的）。
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