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

TAKIFF ALGEBRAS WITH POLYNOMIAL RINGS OF SYMMETRIC INVARIANTS