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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
Abstract

We show that the homology of any Temperley–Lieb algebra 𝒯n(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 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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