Search for a basis of the Temperley-Lieb algebra, using rewriting systems
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914008561352704 |
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| author | Thiebaut, Julien |
| author_facet | Thiebaut, Julien |
| contents | We begin by defining Temperley-Lieb algebra, in two different ways: as a presented algebra or as a diagrammatic algebra. Next, we look for a basis algorithmically, using rewriting theory. Finally, we introduce a generalization of the Temperley-Lieb algebra, which is an oriented version of the previous one. This pushes us to employ a more efficient tool, category theory, to use rewriting to easily obtain a basis for the algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19360 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Search for a basis of the Temperley-Lieb algebra, using rewriting systems Thiebaut, Julien Representation Theory We begin by defining Temperley-Lieb algebra, in two different ways: as a presented algebra or as a diagrammatic algebra. Next, we look for a basis algorithmically, using rewriting theory. Finally, we introduce a generalization of the Temperley-Lieb algebra, which is an oriented version of the previous one. This pushes us to employ a more efficient tool, category theory, to use rewriting to easily obtain a basis for the algebra. |
| title | Search for a basis of the Temperley-Lieb algebra, using rewriting systems |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2508.19360 |