Even Temperley-Lieb algebras and the dga of planar loops
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911259667988480 |
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| author | Boyd, Rachael Boyde, Guy Randal-Williams, Oscar Sroka, Robin J. |
| author_facet | Boyd, Rachael Boyde, Guy Randal-Williams, Oscar Sroka, Robin J. |
| contents | We show that the homology of a Temperley-Lieb algebra on an even number of strands has a rich algebraic structure and is highly nontrivial in general. This is achieved by proving that it is entirely governed by a differential graded algebra: the differential graded algebra of planar loops. We provide a small model for this dga, and use it to obtain consequences on homology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08550 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Even Temperley-Lieb algebras and the dga of planar loops Boyd, Rachael Boyde, Guy Randal-Williams, Oscar Sroka, Robin J. Algebraic Topology Representation Theory 20J06, 16E40, 16E45 We show that the homology of a Temperley-Lieb algebra on an even number of strands has a rich algebraic structure and is highly nontrivial in general. This is achieved by proving that it is entirely governed by a differential graded algebra: the differential graded algebra of planar loops. We provide a small model for this dga, and use it to obtain consequences on homology. |
| title | Even Temperley-Lieb algebras and the dga of planar loops |
| topic | Algebraic Topology Representation Theory 20J06, 16E40, 16E45 |
| url | https://arxiv.org/abs/2511.08550 |