Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deformations of infinite-dimensional Lie algebras, exotic cohomology and
  integrable nonlinear partial differential equations. II   We consider the four-dimensional reduced quasi-classical self-dual
Yang--Mills equation and show that non-triviality of the second exotic
cohomology group of its symmetry algebra implies existence of a two-component
integrable generalization of this equation. The sequence of natural extensions
of this symmetry algebra generate an integrable hierarchy of multi-dimensional
nonlinear PDEs. We write out the first three elements of this hierarchy.

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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: math
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom