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Jordan--Kronecker invariants for Lie algebras of small dimensions
Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2021) no. 4, pp. 73-86.

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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 $\mathfrak{g}$ 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 $(A - \lambda B)(x)$, 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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     author = {A. Yu. Groznova},
     title = {Jordan--Kronecker invariants for {Lie} algebras of small dimensions},
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A. Yu. Groznova. Jordan--Kronecker invariants for Lie algebras of small dimensions. Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2021) no. 4, pp. 73-86. http://geodesic.mathdoc.fr/item/FPM_2021_23_4_a4/

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