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Fusion Categories over Non-Algebraically Closed Fields

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arxiv 2401.02354 v3 pith:JRFR32AL submitted 2024-01-04 math.QA

Sean Sanford This is my paper · ORCID
classification math.QA
keywords categoriesclosedfieldsfusionwhenaccommodateadaptalgebraically
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Several complications arise when attempting to work with fusion categories over arbitrary fields. Here we describe some of the new phenomena that occur when the field is not algebraically closed, and we adapt tools such as the Frobenius-Perron dimension in order to accommodate these new effects.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Classification of symmetric fusion categories over $\mathbb{R}$

    math.QA 2026-08 conditional novelty 7.0 of 10

    Every symmetric fusion category over R is equivalent to the semi-linear super representation category of a Z2-graded finite super group.

  2. Compact Semisimple Tensor 2-Categories are Morita Connected

    math.QA 2024-12 conditional novelty 7.0 of 10

    Every compact semisimple tensor 2-category is Morita equivalent to a connected one over arbitrary fields of characteristic zero, with applications to Witt groups and Galois cohomology.

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