论文标题
motzkin代数和$ a_n $张量类别类别
Motzkin Algebras and the $A_n$ Tensor Categories of Bimodules
论文作者
论文摘要
我们通过引入一系列依恋和基本结构来讨论motzkin代数$ m_k（d）$的结构。我们表明，$ \ cup_ {k \ geq 1} m_k（d）$在且仅当$ d \ in \ in \ {2 \ cos（π/n）+1 | n \ geq 3 \ geq 3 \} \ cup [3，\ infty）$ and Ictiact Ictiact of $ d $的较高换入时才接受因子跟踪。然后构建了一个因素上的不可还原双模型的家族。具有$ a_n $融合规则的张量类别是从这些双模型中获得的。
We discuss the structure of the Motzkin algebra $M_k(D)$ by introducing a sequence of idempotents and the basic construction. We show that $\cup_{k\geq 1}M_k(D)$ admits a factor trace if and only if $D\in \{2\cos(π/n)+1|n\geq 3\}\cup [3,\infty)$ and higher commutants of these factors depend on $D$. Then a family of irreducible bimodules over the factors are constructed. A tensor category with $A_n$ fusion rule is obtained from these bimodules.
