Geodesic
Systems of $sl(2,\mathbb{C})$ tops as two-particle systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 157 (2008) no. 1, pp. 8-21

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We show that Euler–Arnold tops on the algebra $sl(2,\mathbb C)$ are equivalent to a two-particle system of Calogero type. We show that an arbitrary quadratic Hamiltonian of an $sl(2,\mathbb C)$ top can be reduced to one of the three canonical Hamiltonians using the automorphism group of the algebra. For each canonical Hamiltonian, we obtain the corresponding two-particle system and write the bosonization formulas for the coadjoint orbits explicitly. We discuss the relation of the obtained formulas to nondynamical Antonov–Zabrodin–Hasegawa $R$-matrices for Calogero–Sutherland systems.
Keywords: integrable system, Euler–Arnold top
Mots-clés : Calogero–Moser system. 
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     author = {A. V. Smirnov},
     title = {Systems of $sl(2,\mathbb{C})$ tops as two-particle systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {8--21},
     publisher = {mathdoc},
     volume = {157},
     number = {1},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2008_157_1_a1/}
}
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A. V. Smirnov. Systems of $sl(2,\mathbb{C})$ tops as two-particle systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 157 (2008) no. 1, pp. 8-21. http://geodesic.mathdoc.fr/item/TMF_2008_157_1_a1/