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arXiv · 2202.08799

The homology of a Temperley-Lieb algebra on an odd number of strands

Robin J. Sroka
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Abstract

We show that the homology of any Temperley-Lieb algebra $\mathcal{TL}_n(a)$ on an odd number of strands vanishes in positive degrees. This improves a result obtained by Boyd-Hepworth. In addition we present alternative arguments for the following two vanishing results of Boyd-Hepworth. (1) The stable homology of Temperley-Lieb algebras is trivial. (2) If the parameter $a \in R$ is a unit, then the homology of any Temperley-Lieb algebra is concentrated in degree zero.

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Robin J. Sroka. 2022-02-17. The homology of a Temperley-Lieb algebra on an odd number of strands. https://doi.org/10.2140/agt.2024.24.3527

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