Geodesic
Complete commutative subalgebras in polynomial Poisson algebras: a proof of the Mischenko--Fomenko conjecture
Theoretical and applied mechanics, Tome 43 (2016) no. 2, p. 145 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Voir la notice de l'article

The Mishchenko--Fomenko conjecture says that for each real or complex finite-dimensional Lie algebra $\mathfrak g$ there exists a complete set of commuting polynomials on its dual space $\mathfrak g^*$. In terms of the theory of integrable Hamiltonian systems this means that the dual space $\mathfrak g^*$ endowed with the standard Lie--Poisson bracket admits polynomial integrable Hamiltonian systems. This conjecture was proved by S. T.~Sadetov in 2003. Following his idea, we give an explicit geometric construction for commuting polynomials on $\mathfrak g^*$ and consider some examples.
DOI : 10.2298/TAM161111012B
Classification : 37J35, 17B80, 70H06, 53D17, 17B63
Keywords: Poisson-Lie bracket, complete integrability, field extension, Mischenko-Fomenko conjecture, chains of subalgebras, shifting of argument 
@article{10_2298_TAM161111012B,
     author = {Alexey V. Bolsinov},
     title = {Complete commutative subalgebras in polynomial {Poisson} algebras: a proof of the {Mischenko--Fomenko} conjecture},
     journal = {Theoretical and applied mechanics},
     pages = {145 },
     year = {2016},
     volume = {43},
     number = {2},
     doi = {10.2298/TAM161111012B},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/TAM161111012B/}
}
TY  - JOUR
AU  - Alexey V. Bolsinov
TI  - Complete commutative subalgebras in polynomial Poisson algebras: a proof of the Mischenko--Fomenko conjecture
JO  - Theoretical and applied mechanics
PY  - 2016
SP  - 145 
VL  - 43
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.2298/TAM161111012B/
DO  - 10.2298/TAM161111012B
LA  - en
ID  - 10_2298_TAM161111012B
ER  - 
%0 Journal Article
%A Alexey V. Bolsinov
%T Complete commutative subalgebras in polynomial Poisson algebras: a proof of the Mischenko--Fomenko conjecture
%J Theoretical and applied mechanics
%D 2016
%P 145 
%V 43
%N 2
%U http://geodesic.mathdoc.fr/articles/10.2298/TAM161111012B/
%R 10.2298/TAM161111012B
%G en
%F 10_2298_TAM161111012B
Alexey V. Bolsinov. Complete commutative subalgebras in polynomial Poisson algebras: a proof of the Mischenko--Fomenko conjecture. Theoretical and applied mechanics, Tome 43 (2016) no. 2, p. 145 . doi: 10.2298/TAM161111012B

Cité par Sources :