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arXiv · 2511.08550

Even Temperley-Lieb algebras and the dga of planar loops

Rachael Boyd·Guy Boyde·Oscar Randal-Williams·Robin J. Sroka
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Abstract

We show that the homology of a Temperley-Lieb algebra on an even number of strands has a rich algebraic structure and is highly nontrivial in general. This is achieved by proving that it is entirely governed by a differential graded algebra: the differential graded algebra of planar loops. We provide a small model for this dga, and use it to obtain consequences on homology.

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Rachael Boyd, Guy Boyde, Oscar Randal-Williams, Robin J. Sroka. 2025-11-11. Even Temperley-Lieb algebras and the dga of planar loops. https://arxiv.org/abs/2511.08550

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