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arXiv · 2312.13796

Reconstructing algebra objects from NIM-reps in pointed, near-group and quantum group-like fusion categories

Samuel Hannah·Ana Ros Camacho·with an appendix with Devi Young
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Abstract

In this article we study the possible Morita equivalence classes of algebras in three families of fusion categories (pointed, near-group and $A \left( 1,l \right)_{\frac{1}{2}}$) by studying the Non-negative Integer Matrix representations (NIM-reps) of their underlying fusion ring, and compare these results with existing classification results of algebra objects. Also, in an appendix we include a test of the exponents conjecture for modular tensor categories of rank up to 4.

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BibTeXRIS

Samuel Hannah, Ana Ros Camacho, with an appendix with Devi Young. 2023-12-21. Reconstructing algebra objects from NIM-reps in pointed, near-group and quantum group-like fusion categories. https://arxiv.org/abs/2312.13796

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