Towards higher Frobenius functors for symmetric tensor categories

2024/05/29 by Coulembier, Kevin, Flake, Johannes · 3 citations
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2405.19506

Abstract

We develop theory and examples of monoidal functors on tensor categories in positive characteristic that generalise the Frobenius functor from \citeOs, EOf, Tann. The latter has proved to be a powerful tool in the ongoing classification of tensor categories of moderate growth, and we demonstrate the similar potential of the generalisations. More explicitly, we describe a new construction of the generalised Verlinde categories Ver_pⁿ in terms of representation categories of elementary abelian p-groups. This leads to families of functors relating to Ver_pⁿ that we conjecture, and partially show, to exhibit the characteristic properties of the Frobenius functor relating to Ver_p. In particular, we conjecture some of these functors to detect categories that fibre over Ver_pⁿ.

Cited by

• Tensor ideals of abelian type and quantum groups
• Semisimplifying categorical Heisenberg actions and periodic equivalences
• A conjecture on the tensor ideal for an elementary p-group generated by the restriction of a Steinberg module

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