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Decomposing Frobenius Heisenberg categories by:1 (Source: Crossref)

    We give two alternate presentations of the Frobenius Heisenberg category, eisF,k, defined by Savage, when the Frobenius algebra F=F1Fn decomposes as a direct sum of Frobenius subalgebras. In these alternate presentations, the morphism spaces of eisF,k are given in terms of planar diagrams consisting of strands “colored” by integers i=1,,n, where a strand of color i carries tokens labelled by elements of Fi. In addition, we prove that when F decomposes this way, the tensor product of Frobenius Heisenberg categories, eisF1,keisFn,k, is equivalent to a certain subcategory of the Karoubi envelope of eisF,k that we call the partial Karoubi envelope of eisF,k.

    Communicated by J. Brundan

    AMSC: 18D10