Two body systems from sl(2,C)-tops

Details Two body systems from sl(2,C)-tops Two body systems from sl(2,C)-tops

2007-11-15

arxiv.org/abs/0711.2432v1

Mathematics

Dynamical Systems

9 pages

Scientific paper

It is shown that sl(2,$\mathbb{C}$) Euler-Arnold tops are equivalent to the two-body systems of Calogero-Moser type. We prove that generic Hamiltonians of sl(2,$\mathbb{C}$) tops are equivalent to one of three canonical Hamiltonians. For all canonical Hamiltonians the corresponding two-body system is found. Bosonisation formulas for each case are obtained explicitly. Relations with Antonov-Zabrodin-Hasegawa R-matrix are discussed.

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