Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On dynamical r-matrices obtained from Dirac reduction and their
  generalizations to affine Lie algebras   According to Etingof and Varchenko, the classical dynamical Yang-Baxter
equation is a guarantee for the consistency of the Poisson bracket on certain
Poisson-Lie groupoids. Here it is noticed that Dirac reductions of these
Poisson manifolds give rise to a mapping from dynamical r-matrices on a pair
$\L\subset \A$ to those on another pair $\K\subset \A$, where $\K\subset
\L\subset \A$ is a chain of Lie algebras for which $\L$ admits a reductive
decomposition as $\L=\K+\M$. Several known dynamical r-matrices appear
naturally in this setting, and its application provides new r-matrices, too. In
particular, we exhibit a family of r-matrices for which the dynamical variable
lies in the grade zero subalgebra of an extended affine Lie algebra obtained
from a twisted loop algebra based on an arbitrary finite dimensional self-dual
Lie algebra.

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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: stat
13
The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
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The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom