Motzkin Algebras and the $A_n$ Tensor Categories of Bimodules

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 ${\cup }_{k\ge 1}{M}_k(D)$ admits a factor trace if and only if $D\in \{2\cos (\pi /n)+1|n\ge 3\}\cup [3,\infty )$ 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.

47 pages

References in corpus (2)

• A categorical and diagrammatical approach to Temperley-Lieb algebras
• Traces On Diagram Algebras I: Free Partition Quantum Groups, Random Lattice Paths And Random Walks On Trees

Cited by in corpus (1)

• The Motzkin subproduct system