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arXiv · 1706.06904

Semisimple and separable algebras in multi-fusion categories

Liang Kong·Hao Zheng
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Abstract

We give a classification of semisimple and separable algebras in a multi-fusion category over an arbitrary field in analogy to Wedderben-Artin theorem in classical algebras. It turns out that, if the multi-fusion category admits a semisimple Drinfeld center, the only obstruction to the separability of a semisimple algebra arises from inseparable field extensions as in classical algebras. Among others, we show that a division algebra is separable if and only if it has a nonvanishing dimension.

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Liang Kong, Hao Zheng. 2017-06-21. Semisimple and separable algebras in multi-fusion categories. https://arxiv.org/abs/1706.06904

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