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arXiv · 2008.04487

Motzkin Algebras and the $A_n$ Tensor Categories of Bimodules

Vaughan F. R. Jones·Jun Yang
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Abstract

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 $D\in \{2\cos(\pi/n)+1|n\geq 3\}\cup [3,\infty)$ 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.

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BibTeXRIS

Vaughan F. R. Jones, Jun Yang. 2020-08-11. Motzkin Algebras and the $A_n$ Tensor Categories of Bimodules. https://doi.org/10.1142/s0129167x21500774

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