Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Groenewold-Moyal Product, \alpha^\star-Cohomology, and Classification of
  Translation-Invariant Non-Commutative Structures   The theory of alpha_star-cohomology is studied thoroughly and it is shown
that in each cohomology class there exists a unique 2-cocycle, the harmonic
form, which generates a particular Groenewold-Moyal star product. This leads to
an algebraic classification of translation-invariant non-commutative structures
and shows that any general translationinvariant non-commutative quantum field
theory is physically equivalent to a Groenewold- Moyal non-commutative quantum
field theory.

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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: eess
29
The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat