Abstract
We study the \(G\)-extensions \(\mathcal{C}\) of a near-group fusion category of type \((\mathbb{Z}_2,1)\). If \(\mathcal{C}\) is braided we prove that \(\mathcal{C}\) can be reconstructed from pointed fusion categories by \(\mathbb{Z}_2\)-extensions or \(\mathbb{Z}_2\)-equivariantizations. Furthermore, if \(\mathcal{C}\) is also integral, or \(\mathcal{C}\) is equivalent as a tensor category to the category of finite dimensional representations of a semisimple Hopf algebra, we prove that \(\mathcal{C}\) is group-theoretical, which completes the classification of these categories in the sense of Morita equivalence.
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Dai, L. Extensions of a near-group category of type \((\mathbb{Z}_2,1)\). Acta Math. Hungar. 167, 404–418 (2022). https://doi.org/10.1007/s10474-022-01256-9
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DOI: https://doi.org/10.1007/s10474-022-01256-9