Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Radon-Nikodym type theorem for $\alpha$-completely positive maps on
  groups   We show that an operator valued $\alpha$-completely positive map on a group G
is given by a unitary representation of G on a Krein space which satisfies some
condition. Moreover, two unitary equivalent such unitary representations define
the same {\alpha}-completely positive map. Also we introduce a pre-order
relation on the collection of {\alpha}-completely positive maps on a group and
we characterize this relation in terms of the unitary representation associated
to each map.

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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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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: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio