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Classification of $mathfrak{sl}_3$ relations in the Witt group of nondegenerate braided fusion categories

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 نشر من قبل Andrew Schopieray
 تاريخ النشر 2016
  مجال البحث
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 تأليف Andrew Schopieray




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The Witt group of nondegenerate braided fusion categories $mathcal{W}$ contains a subgroup $mathcal{W}_text{un}$ consisting of Witt equivalence classes of pseudo-unitary nondegenerate braided fusion categories. For each finite-dimensional simple Lie algebra $mathfrak{g}$ and positive integer $k$ there exists a pseudo-unitary category $mathcal{C}(mathfrak{g},k)$ consisting of highest weight integerable $hat{g}$-modules of level $k$ where $hat{mathfrak{g}}$ is the corresponding affine Lie algebra. Relations between the classes $[mathcal{C}(mathfrak{sl}_2,k)]$, $kgeq1$ have been completely described in the work of Davydov, Nikshych, and Ostrik. Here we give a complete classification of relations between the classes $[mathcal{C}(mathfrak{sl}_3,k)]$, $kgeq1$ with a view toward extending these methods to arbitrary simple finite dimensional Lie algebras $mathfrak{g}$ and positive integer levels $k$.



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