English

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