Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quadratic relations of the deformed $W$-superalgebra ${\cal W}_{q,
  t}(\mathfrak{sl}(2|1))$   We revisit the free field construction of the deformed $W$-superalgebras
${\cal W}_{q,t}(\mathfrak{sl}(2|1))$ by J. Ding and B. Feigin, {\it
Contemp.Math.}{\bf 248}, 83-108 (1998), where the basic $W$-current and
screening currents have been found. In this paper we introduce higher
$W$-currents and obtain a closed set of quadratic relations among them. These
relations are independent of the choice of Dynkin diagrams for the superalgebra
$\mathfrak{sl}(2|1)$, though the screening currents are not. This allows us to
define ${\cal W}_{q,t}(\mathfrak{sl}(2|1))$ by generators and relations.

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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph