Geodesic
Verification of the generalized hypothesis of Mishchenko--Fomenko for Lie algebras of small dimension
Čebyševskij sbornik, Tome 24 (2023) no. 5, pp. 126-135.

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In the case of Lie algebras $\mathfrak{g}$ of small dimension $\leq 7$, an enhanced version of the Generalised argument shift conjecture is proved, namely, it is shown that for any element $a\in\mathfrak{g}^*$ on the dual space $\mathfrak{g}^*$ there is a complete set of polynomials in the bi-involution with respect to the standard Poisson-Lie bracket and the frozen argument bracket associated with the covector $a$.
Keywords: Lie–Poison bracket, compatible Poisson bracket , sets of polynomials in bi-involution. 
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F. I. Lobzin. Verification of the generalized hypothesis of Mishchenko--Fomenko for Lie algebras of small dimension. Čebyševskij sbornik, Tome 24 (2023) no. 5, pp. 126-135. http://geodesic.mathdoc.fr/item/CHEB_2023_24_5_a7/

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