Semisimple and separable algebras in multi-fusion categories
Quantum Algebra
2019-11-22 v2
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.
Keywords
Cite
@article{arxiv.1706.06904,
title = {Semisimple and separable algebras in multi-fusion categories},
author = {Liang Kong and Hao Zheng},
journal= {arXiv preprint arXiv:1706.06904},
year = {2019}
}
Comments
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