The homology of a Temperley-Lieb algebra on an odd number of strands
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866929552347889664 |
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| author | Sroka, Robin J. |
| author_facet | Sroka, Robin J. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_08799 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The homology of a Temperley-Lieb algebra on an odd number of strands Sroka, Robin J. Algebraic Topology 16E40, 20J05 (primary), 20F55 (secondary) 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. |
| title | The homology of a Temperley-Lieb algebra on an odd number of strands |
| topic | Algebraic Topology 16E40, 20J05 (primary), 20F55 (secondary) |
| url | https://arxiv.org/abs/2202.08799 |