2017/06/21 by Liang Kong, Hao Zheng, Kong, Liang +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.1706.06904
openalex publication_date 2017/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.