Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classical R-Matrices and the Feigin-Odesskii Algebra via Hamiltonian and
  Poisson Reductions   We 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.

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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin