Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shapovalov determinant for loop superalgebras   Let a given finite dimensional simple Lie superalgebra g possess an even
invariant non-degenerate supersymmetric bilinear form. We show how to recover
the quadratic Casimir element for the Kac-Moody superalgebra related to the
loop superalgebra with values in g from the quadratic Casimir element for g.
Our main tool here is an explicit Wick normal form of the even quadratic
Casimir operator for the Kac--Moody superalgebra associated with g; this Wick
normal form is of independent interest.
  If g possesses an odd invariant supersymmetric bilinear form we compute the
cubic Casimir element.
  In addition to the cases of Lie superalgebras g(A) with Cartan matrix A for
which the answer was known, we consider the Poisson Lie superalgebra poi(0|n)
and the related Kac--Moody superalgebra.

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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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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: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph