Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Associative forms and second cohomologies of Lie superalgebras $HO$ and
  $KO$   We consider two families of finite-dimensional simple Lie superalgebras of
Cartan type, denoted by HO and KO, over an algebraically closed field of
characteristic p>3. Using the weight space decompositions and the principal
gradings we first show that neither HO nor KO possesses a nondegenerate
associative form. Then, by means of computing the superderivations from the Lie
superalgebras in consideration into their dual modules, the second cohomology
groups with coefficients in the trivial modules are proved to be vanishing.

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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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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: acc-phys
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The categories of this paper are: cs