论文标题
标准$λ$ -lattices，刚性$ {\ rm c}^*$ tensor类别和（bi）模块
Standard $λ$-lattices, rigid ${\rm C}^*$ tensor categories, and (bi)modules
论文作者
论文摘要
在本文中，我们直接从标准的$λ$ - lattice直接构建了一个带有规范统一双函数的2个刚性$ {\ rm c}^*$多发音类别。我们使用无可获取的马尔可夫塔和格子的概念来定义模块和bimodule的概念，而不是标准$λ$ -Lattice（S），我们明确地构建了相关的模块类别和Bimodule类别，而Bimodule类别对相应的2个刚性刚性$ {\ rm c}^*$多Intensor类别。 例如，我们计算了temperley-lieb-jones标准$λ$ - lattices的模块和双模模，以无可抓的马尔可夫塔和格子而言。转化为Bigraded Hilbert空间的单一2类，我们在边缘加权图中恢复了Decommer-Yamshita对$ \ Mathcal {Tlj} $模块的分类，以及$ \ Mathcal {tlj} $ bimodules的$ \ Mathcal {tlj} $ bimodules的分类。 作为应用程序，我们表明每个（无限深度）的平面代数都嵌入其主要图的两部分图平面代数中。
In this article, we construct a 2-shaded rigid ${\rm C}^*$ multitensor category with canonical unitary dual functor directly from a standard $λ$-lattice. We use the notions of traceless Markov towers and lattices to define the notion of module and bimodule over standard $λ$-lattice(s), and we explicitly construct the associated module category and bimodule category over the corresponding 2-shaded rigid ${\rm C}^*$ multitensor category. As an example, we compute the modules and bimodules for Temperley-Lieb-Jones standard $λ$-lattices in terms of traceless Markov towers and lattices. Translating into the unitary 2-category of bigraded Hilbert spaces, we recover DeCommer-Yamshita's classification of $\mathcal{TLJ}$ modules in terms of edge weighted graphs, and a classification of $\mathcal{TLJ}$ bimodules in terms of biunitary connections on square-partite weighted graphs. As an application, we show that every (infinite depth) subfactor planar algebra embeds into the bipartite graph planar algebra of its principal graph.
