Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Super-Affine Hierarchies and their Poisson Embeddings   The link between (super)-affine Lie algebras as Poisson brackets structures
and integrable hierarchies provides both a classification and a tool for
obtaining superintegrable hierarchies. The lack of a fully systematic procedure
for constructing matrix-type Lax operators, which makes the supersymmetric case
essentially different from the bosonic counterpart, is overcome via the notion
of Poisson embeddings (P.E.), i.e. Poisson mappings relating affine structures
to conformal structures (in their simplest version P.E. coincide with the
Sugawara construction). A full class of hierarchies can be recovered by using
uniquely Lie-algebraic notions. The group-algebraic properties implicit in the
super-affine picture allow a systematic derivation of reduced hierarchies by
imposing either coset conditions or hamiltonian constraints (or possibly both).

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The categories of this paper are: math
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: q-fin