On Dehornoy's representation for the Yang-Baxter equation
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908948394672128 |
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| author | Dietzel, Carsten Feingesicht, Edouard Properzi, Silvia |
| author_facet | Dietzel, Carsten Feingesicht, Edouard Properzi, Silvia |
| contents | This article investigates Dehornoy's monomial representations for structure groups and Coxeter-like groups associated with a set-theoretic solution to the Yang--Baxter equation. Using the brace structure of these groups and the language of cycle sets, we prove that the irreducibility of the associated monomial representations is equivalent to the indecomposability of the underlying solutions, except when the Dehornoy class is two. For indecomposable solutions, we show that these representations are induced from certain explicitly constructed one-dimensional representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10648 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Dehornoy's representation for the Yang-Baxter equation Dietzel, Carsten Feingesicht, Edouard Properzi, Silvia Group Theory Quantum Algebra Representation Theory 16T25, 20C15, 20N02, 81R50 This article investigates Dehornoy's monomial representations for structure groups and Coxeter-like groups associated with a set-theoretic solution to the Yang--Baxter equation. Using the brace structure of these groups and the language of cycle sets, we prove that the irreducibility of the associated monomial representations is equivalent to the indecomposability of the underlying solutions, except when the Dehornoy class is two. For indecomposable solutions, we show that these representations are induced from certain explicitly constructed one-dimensional representations. |
| title | On Dehornoy's representation for the Yang-Baxter equation |
| topic | Group Theory Quantum Algebra Representation Theory 16T25, 20C15, 20N02, 81R50 |
| url | https://arxiv.org/abs/2409.10648 |