For an arbitrary representation ρ of a complex finite-dimensional Lie algebra, we construct a collection of numbers that we call the Jordan–Kronecker invariants of ρ. Among other interesting properties, these numbers provide lower bounds for degrees of polynomial invariants of ρ. Furthermore, we prove that these lower bounds are exact if and only if the invariants are independent outside of a set of large codimension. Finally, we show that under certain additional assumptions our bounds are exact if and only if the algebra of invariants is freely generated.

中文翻译：

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李代数表示的 JORDAN-KRONECKER 不变量和不变量多项式的次数

对于任意的表示ρ一个复杂的有限维李代数的，我们构建的数字，我们称之为集合乔丹克罗内克不变的ρ。在其他有趣的属性中，这些数字为ρ的多项式不变量的次数提供了下限。此外，我们证明了这些下界是准确的，当且仅当不变量在一组大的codimension 之外是独立的。最后，我们表明，在某些额外的假设下，当且仅当不变量的代数是自由生成的，我们的边界才是精确的。