Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Free-Boolean independence with amalgamation   In this paper, we develop the notion of free-Boolean independence in an
amalgamation setting. We construct free-Boolean cumulants and show that the
vanishing of mixed free-Boolean cumulants is equivalent to our free-Boolean
independence with amalgamation. We also provide a characterization of
free-Boolean independence by conditions in terms of mixed moments. In addition,
we study free-Boolean independence over a $C^*$-algebra and prove a positivity
property.

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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn