Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The 3 x 3 x 3 hyperdeterminant as a polynomial in the fundamental
  invariants for SL(3,C) x SL(3,C) x SL(3,C)   We briefly review previous work on the invariant theory of 3 x 3 x 3 arrays.
We then recall how to generate arrays of arbitrary size m_1 x ... x m_k with
hyperdeterminant 0. Our main result is an explicit formula for the 3 x 3 x 3
hyperdeterminant as a polynomial in the fundamental invariants of degrees 6, 9
and 12 for the action of the Lie group SL(3,C) x SL(3,C) x SL(3,C). We apply
our calculations to Nurmiev's classification of normal forms for 3 x 3 x 3
arrays.

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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph