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Ore's theorem on subfactor planar algebras
Quantum Topology ( IF 1.0 ) Pub Date : 2020-09-24 , DOI: 10.4171/qt/141
Sébastien Palcoux 1
Affiliation  

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.

中文翻译:

关于子因子平面代数的 Ore 定理

本文证明了具有分布双投影格的不可约子因子平面代数允许生成恒等双投影的最小 2-box 投影。它是 Oystein Ore 关于有限群分布区间的定理 (1938) 的推广(2013 年推测),是 Kenneth S. Brown 在代数组合学 (2000) 中的猜想的自然子因子扩展的推论。我们推导出组合学和有限群论中的表示之间的联系。
更新日期:2020-09-24
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