Abstract
We show that the Drinfeld-Sokolov reduction is equivalent to a bi-Hamiltonian reduction, in the sense that these two reductions, although different, lead to the same reduced Poisson (more correctly, bi-Hamiltonian) structure. In order to do this, we heavily use the fact that they are both particular cases of a Marsden-Ratiu reduction.
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This work has been supported by the Italian MURST and by the GNFM of the Italian CNR.
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Pedroni, M. Equivalence of the Drinfeld-Sokolov reduction to a bi-Hamiltonian reduction. Lett Math Phys 35, 291–302 (1995). https://doi.org/10.1007/BF00750836
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DOI: https://doi.org/10.1007/BF00750836