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arxiv: 0711.4777 · v1 · submitted 2007-11-29 · 🧮 math-ph · math.MP

A Temperley-Lieb category for 2-manifolds

Marcos Alvarez , Paul P. Martin This is my paper
classification 🧮 math-ph math.MP
keywords categoriescategorytemperley-liebcombinatorialcomputationcomputeconsiderationconstruction
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Guided by consideration of problems in 2 and 3 dimensional lattice model computation, we are led to define a number of new categories, and functors between these categories and the partition category, culminating in the introduction of two categories generalising the Temperley-Lieb category. We show how to compute practically in these categories, by giving a combinatorial realisation of their (topological) construction.

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  1. Semisimplicity criterion for 2-tonal partition algebras

    math.RT 2026-04 unverdicted novelty 7.0

    Even partition algebras P_n^2(δ) over ℂ are semisimple for all n if and only if δ is not a non-negative integer.