We discuss the structure of the Motzkin algebra Mk(D) by introducing a sequence of idempotents and the basic construction. We show that ⋃k≥1Mk(D) admits a factor trace if and only if D ∈{2cos(π/n) + 1|n ≥ 3}∪ [3,∞) and the higher commutants of these factors depend on D. Then a family of irreducible bimodules over these factors is constructed. A tensor category with An fusion rule is obtained from these bimodules.

中文翻译：

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Motzkin 代数和双模的张量范畴

我们讨论 Motzkin 代数的结构米ķ(D)通过介绍幂等序列和基本构造。我们表明⋃ķ≥1米ķ(D)当且仅当D ∈{2因(π/n) + 1|n ≥ 3}∪ [3,∞)并且这些因子的高位交换取决于D. 然后在这些因子上构造了一系列不可约双模。一个张量类别一种n融合规则是从这些双模块中获得的。