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arXiv · 2106.16186

Tetrahedral symmetry of 6j-symbols in fusion categories

Jürgen Fuchs·Tobias Grøsfjeld
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Abstract

We establish tetrahedral symmetries of 6j-symbols for arbitrary fusion categories under minimal assumptions. As a convenient tool for our calculations we introduce the notion of a veined fusion category, which is generated by a finite set of simple objects but is larger than its skeleton. Every fusion category C contains veined fusion subcategories that are monoidally equivalent to C and which suffice to compute many categorical properties for C. The notion of a veined fusion category does not assume the presence of a pivotal structure, and thus in particular does not assume unitarity. We also exhibit the geometric origin of the algebraic statements for the 6j-symbols.

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Jürgen Fuchs, Tobias Grøsfjeld. 2021-06-30. Tetrahedral symmetry of 6j-symbols in fusion categories. https://arxiv.org/abs/2106.16186

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