Ore's theorem on subfactor planar algebras

Abstract

This article proves that an irreducible subfactor planar algebra with a distributive biprojection lattice admits a minimal 2-box projection generating the identity biprojection. It is a generalization (conjectured in 2013) of a theorem of Oystein Ore on distributive intervals of finite groups (1938), and a corollary of a natural subfactor extension of a conjecture of Kenneth S. Brown in algebraic combinatorics (2000). We deduce a link between combinatorics and representations in finite group theory.

14 pages. It reproduces some preliminaries of arXiv:1702.02124 and arXiv:1703.04486, for being self-contained

References in corpus (6)

• Noncommutative Uncertainty Principles
• Order complexes of coset posets of finite groups are not contractible
• Ore's theorem on cyclic subfactor planar algebras and beyond
• Ore's theorem for cyclic subfactor planar algebras and applications
• Dual Ore's theorem on distributive intervals of finite groups
• Dual Ore's theorem for distributive intervals of small index

Cited by in corpus (3)

• Interpolated family of non group-like simple integral fusion rings of Lie type
• Dual Ore's theorem on distributive intervals of finite groups
• Euler totient of subfactor planar algebras