Noncommutative Minkowski integral inequality and a unitary categorification criterion for fusion rings
Operator Algebras
2026-01-22 v2 Category Theory
Functional Analysis
Quantum Algebra
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.
Keywords
Cite
@article{arxiv.2601.13490,
title = {Noncommutative Minkowski integral inequality and a unitary categorification criterion for fusion rings},
author = {Junhwi Lim},
journal= {arXiv preprint arXiv:2601.13490},
year = {2026}
}
Comments
14 pages, two large tables