Abstract
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.
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The research of the first author was carried out at the IITP RAS at the expense of the Russian Foundation for Sciences — project number 14-50-00150.
Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) — project number 330450448.
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PANYUSHEV, D.I., YAKIMOVA, O.S. TAKIFF ALGEBRAS WITH POLYNOMIAL RINGS OF SYMMETRIC INVARIANTS. Transformation Groups 25, 609–624 (2020). https://doi.org/10.1007/s00031-019-09532-9
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DOI: https://doi.org/10.1007/s00031-019-09532-9