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arXiv · 2601.13490

Noncommutative Minkowski integral inequality and a unitary categorification criterion for fusion rings

Junhwi Lim
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Abstract

We prove a noncommutative analogue of Minkowski's integral inequality for commuting squares of tracial von Neumann algebras. The inequality implies a necessary condition for a quadruple of graphs to be realized as inclusion graphs of a commuting square of multi-matrix algebras. As a corollary, we obtain a unitary categorification criterion for based rings, in particular, fusion rings.

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Junhwi Lim. 2026-01-20. Noncommutative Minkowski integral inequality and a unitary categorification criterion for fusion rings. https://arxiv.org/abs/2601.13490

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