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

Sroka, Robin J

doi:10.2140/agt.2024.24.3527

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

Robin J Sroka

Algebraic & Geometric Topology 24 (2024) 3527–3541

DOI: 10.2140/agt.2024.24.3527

Abstract

We show that the homology of any Temperley–Lieb algebra ${𝒯 ℒ}_{n} (a)$ on an odd number of strands vanishes in positive degrees. This improves a result obtained by Boyd and Hepworth. In addition, we present alternative arguments for two vanishing results of Boyd and Hepworth: the stable homology of Temperley–Lieb algebras is trivial, and if the parameter $a \in R$ is a unit, then the homology of any Temperley–Lieb algebra is concentrated in degree zero.

Keywords

homology, homological stability, Temperley–Lieb algebra

Mathematical Subject Classification

Primary: 16E40, 20J05

Secondary: 20F55

References

Publication

Received: 31 July 2022

Revised: 29 August 2022

Accepted: 31 October 2022

Published: 7 October 2024

Authors

Robin J Sroka
Department of Mathematics and Statistics McMaster University Hamilton, ON Canada	Mathematisches Institut Universität Münster Münster Germany

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Volume 24, issue 6 (2024)