Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lifting theorem for the virtual pure braid groups   In this article we prove theorem on Lifting for the set of virtual pure braid
groups. This theorem says that if we know presentation of virtual pure braid
group $VP_4$, then we can find presentation of $VP_n$ for arbitrary $n > 4$.
Using this theorem we find the set of generators and defining relations for
simplicial group $T_*$ which was defined in the previuos article of the
authors. We find a decomposition of the Artin pure braid group $P_n$ in
semi-direct product of free groups in the cabled generators.

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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: physics