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

Abstract

We show that the homology of any Temperley-Lieb algebra ${\mathcal{T}\mathcal{L}}_n(a)$ 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.

arXiv commentv2: 13 pages, 6 figures. Updated following referee's suggestions. Improved exposition and notation. Accepted version, to appear in Algebraic & Geometric Topology

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Cited by in corpus (1)

• Stable homology isomorphisms for the partition and Jones annular algebras