The homology of a Temperley-Lieb algebra on an odd number of strands
Abstract
We show that the homology of any Temperley-Lieb algebra TLn(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 ∈ R is a unit, then the homology of any Temperley-Lieb algebra is concentrated in degree zero.
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