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On braided tensor categories of type BCD

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arxiv math/0301142 v3 pith:5PFJAVOM submitted 2003-01-14 math.QA math.RAmath.RT

Imre Tuba , Hans Wenzl This is my paper · ORCID
classification math.QAmath.RAmath.RT
keywords braidingcategoriesbraideddeterminedsymmetrictensoraffectallows
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We give a full classification of all braided semisimple tensor categories whose Grothendieck semiring is the one of Rep(O(\infty) (formally), Rep(O(N), Rep(Sp(N) or of one of its associated fusion categories. If the braiding is not symmetric, they are completely determined by the eigenvalues of a certain braiding morphism, and we determine precisely which values can occur in the various cases. If the category allows a symmetric braiding, it is essentially determined by the dimension of the object corresponding to the vector representation. Note that the paper is followed by a brief erratum, which corrects a mistake, which does not affect the main results of the paper.

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  1. The quantum spin Brauer category

    math.QA 2025-04 accept novelty 7.0 of 10

    The quantum spin Brauer category is a braided diagrammatic category whose Karoubi completion covers all finite-dimensional U_q(so(N)) and U_q(o(N)) modules, including spin modules.

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