Extending results of Rais–Tauvel, Macedo–Savage, and Arakawa–Premet, we prove that under mild restrictions on the Lie algebra \( \mathfrak{q} \) having the polynomial ring of symmetric invariants, the m-th Takiff algebra of \( \mathfrak{q} \), \( \mathfrak{q} \)⟨m⟩, also has a polynomial ring of symmetric invariants.

中文翻译：

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具有对称不变式多项式环的塔基夫代数

扩展Rais–Tauvel，Macedo–Savage和Arakawa–Premet的结果，我们证明，在具有对称不变式多项式环的Lie代数\（\ mathfrak {q} \）的适度限制下，第m个Takiff代数\（\ mathfrak {q} \） ，\（\ mathfrak {q} \） ⟨米⟩，还具有对称的不变量的多项式环。