Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Review of deformation theory I: Concrete formulas for deformations of
  algebraic structures   In this review article, first we give the concrete formulas of
representations and cohomologies of associative algebras, Lie algebras, pre-Lie
algebras, Leibniz algebras and 3-Lie algebras and some of their strong homotopy
analogues. Then we recall the graded Lie algebras and graded associative
algebras that characterize these algebraic structures as Maurer-Cartan
elements. The corresponding Maurer-Cartan element equips the graded Lie or
associative algebra with a differential. Then the deformations of the given
algebraic structures are characterized as the Maurer-Cartan elements of the
resulting differential graded Lie or associative algebras. We also recall the
relation between the cohomologies and the differential graded Lie and
associative algebras that control the deformations.

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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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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: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int