Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $ \mathbb{Z}_2 \times \mathbb{Z}_2 $ generalizations of ${\cal N} = 1$
  superconformal Galilei algebras and their representations   We introduce two classes of novel color superalgebras of $ \mathbb{Z}_2
\times \mathbb{Z}_2 $ grading. This is done by realizing members of each in the
universal enveloping algebra of the ${\cal N}=1$ supersymmetric extension of
the conformal Galilei algebra. This allows us to upgrade any representation of
the super conformal Galilei algebras to a representation of the $ \mathbb{Z}_2
\times \mathbb{Z}_2 $ graded algebra. As an example, boson-fermion Fock space
representation of one class is given. We also provide a vector field
realization of members of the other class by using a generalization of the
Grassmann calculus to $ \mathbb{Z}_2 \times \mathbb{Z}_2 $ graded setting.

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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: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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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: chem-ph
13
The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
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The categories of this paper are: eess
3
The categories of this paper are: physics
1
The categories of this paper are: cs