H W Braden et al 2003 J. Phys. A: Math. Gen. 36 6979 doi:10.1088/0305-4470/36/25/306
Classical r-matrices and the Feigin–Odesskii algebra via Hamiltonian and Poisson reductions
H W Braden1, V A Dolgushev2,3, M A Olshanetsky3 and A V Zotov3
Show affiliationsWe present a formula for a classical r-matrix of an integrable system obtained by Hamiltonian reduction of some free field theories using pure gauge symmetries. The framework of the reduction is restricted only by the assumption that the respective gauge transformations are Lie group ones. Our formula is in terms of Dirac brackets, and some new observations on these brackets are made. We apply our method to derive a classical r-matrix for the elliptic Calogero–Moser system with spin starting from the Higgs bundle over an elliptic curve with marked points. In the paper, we also derive a classical Feigin–Odesskii algebra by a Poisson reduction of some modification of the Higgs bundle over an elliptic curve. This allows us to include integrable lattice models in a Hitchin-type construction.
- PACS
- MSC
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81R50 Quantum groups and related algebraic methods (See also 16W35, 17B37)
15A90 Applications of matrix theory to physics
22E60 Lie algebras of Lie groups (For the algebraic theory of Lie algebras, see 17Bxx)
- Subjects
- Dates
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Issue 25 (27 June 2003)
Received 21 January 2003, in final form 8 May 2003
Published 12 June 2003
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Classical r-matrices and the Feigin–Odesskii algebra via Hamiltonian and Poisson reductions
H W Braden et al 2003 J. Phys. A: Math. Gen. 36 6979
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