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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{CHEB_2023_24_5_a7,
     author = {F. I. Lobzin},
     title = {Verification of the generalized hypothesis of {Mishchenko--Fomenko} for {Lie} algebras of small dimension},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {126--135},
     publisher = {mathdoc},
     volume = {24},
     number = {5},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2023_24_5_a7/}
}
TY  - JOUR
AU  - F. I. Lobzin
TI  - Verification of the generalized hypothesis of Mishchenko--Fomenko for Lie algebras of small dimension
JO  - Čebyševskij sbornik
PY  - 2023
SP  - 126
EP  - 135
VL  - 24
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2023_24_5_a7/
LA  - ru
ID  - CHEB_2023_24_5_a7
ER  - 
%0 Journal Article
%A F. I. Lobzin
%T Verification of the generalized hypothesis of Mishchenko--Fomenko for Lie algebras of small dimension
%J Čebyševskij sbornik
%D 2023
%P 126-135
%V 24
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2023_24_5_a7/
%G ru
%F CHEB_2023_24_5_a7
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/