Takiff algebras with polynomial rings of symmetric invariants

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.

arXiv comment17 pages