Geodesic
Integrable $sl(N,\mathbb C)$ tops as Calogero–Moser systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 3, pp. 355-369 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We show a relation between systems of integrable tops on the algebras $sl(N,\mathbb C)$ and Calogero–Moser systems of $N$ particles. We construct classical Lax operators corresponding to these systems. We show that these operators are related to certain new trigonometric and rational solutions of the Yang–Baxter equations for the algebras $sl(N,\mathbb C)$ and give explicit formulas for $N=2,3$.
Keywords: integrable system, Euler–Arnold top, Yang–Baxter equation. 
@article{TMF_2009_158_3_a2,
     author = {A. V. Smirnov},
     title = {Integrable $sl(N,\mathbb C)$ tops as {Calogero{\textendash}Moser} systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {355--369},
     year = {2009},
     volume = {158},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_158_3_a2/}
}
TY  - JOUR
AU  - A. V. Smirnov
TI  - Integrable $sl(N,\mathbb C)$ tops as Calogero–Moser systems
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2009
SP  - 355
EP  - 369
VL  - 158
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2009_158_3_a2/
LA  - ru
ID  - TMF_2009_158_3_a2
ER  - 
%0 Journal Article
%A A. V. Smirnov
%T Integrable $sl(N,\mathbb C)$ tops as Calogero–Moser systems
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2009
%P 355-369
%V 158
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2009_158_3_a2/
%G ru
%F TMF_2009_158_3_a2
A. V. Smirnov. Integrable $sl(N,\mathbb C)$ tops as Calogero–Moser systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 3, pp. 355-369. http://geodesic.mathdoc.fr/item/TMF_2009_158_3_a2/

[1] A. Smirnov, Two-body systems from $sl(2,\mathbb C)$-tops, arXiv: 0711.2432

[2] V. I. Arnold, Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1989 | MR | MR | Zbl

[3] A. Smirnov, Correspondece between Calogero–Moser systems and integrable $SL(N,\mathbb C)$ Euler–Arnold tops, arXiv: 0809.2187 | MR

[4] A. M. Levin, M. A. Olshanetsky, A. Zotov, Comm. Math. Phys., 236:1 (2003), 93–133 | DOI | MR | Zbl

[5] N. Hitchin, Duke Math. J., 54:1 (1987), 91–114 | DOI | MR | Zbl

[6] A. Antonov, K. Hasegawa, A. Zabrodin, Nucl. Phys. B, 503:3 (1997), 747–770 ; arXiv: hep-th/9704074 | DOI | MR | Zbl

[7] A. Gorsky, A. Zabrodin, J. Phys. A, 26:15 (1993), L635–L640 ; arXiv: hep-th/9303026 | DOI | MR | Zbl