Back to baxterisation
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2017
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| _version_ | 1866915192776949760 |
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| author | Crampe, N. Ragoucy, E. Vanicat, M. |
| author_facet | Crampe, N. Ragoucy, E. Vanicat, M. |
| contents | In the continuity of our previous paper arXiv:1509.05516, we define three new algebras, $A_{n}(a,b,c)$, $B_{n}$ and $C_{n}$, that are close to the braid algebra. They allow to build solutions to the braided Yang-Baxter equation with spectral parameters. The construction is based on a baxterisation procedure, similar to the one used in the context of Hecke or BMW algebras.
The $A_{n}(a,b,c)$ algebra depends on three arbitrary parameters, and when the parameter $a$ is set to zero, we recover the algebra $M_{n}(b,c)$ already introduced elsewhere for purpose of baxterisation. The Hecke algebra (and its baxterisation) can be recovered from a coset of the $A_{n}(0,0,c)$ algebra. The algebra $A_{n}(0,b,-b^2)$ is a coset of the braid algebra.
The two other algebras $B_{n}$ and $C_{n}$ do not possess any parameter, and can be also viewed as a coset of the braid algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1708_02754 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Back to baxterisation Crampe, N. Ragoucy, E. Vanicat, M. Mathematical Physics Quantum Algebra In the continuity of our previous paper arXiv:1509.05516, we define three new algebras, $A_{n}(a,b,c)$, $B_{n}$ and $C_{n}$, that are close to the braid algebra. They allow to build solutions to the braided Yang-Baxter equation with spectral parameters. The construction is based on a baxterisation procedure, similar to the one used in the context of Hecke or BMW algebras. The $A_{n}(a,b,c)$ algebra depends on three arbitrary parameters, and when the parameter $a$ is set to zero, we recover the algebra $M_{n}(b,c)$ already introduced elsewhere for purpose of baxterisation. The Hecke algebra (and its baxterisation) can be recovered from a coset of the $A_{n}(0,0,c)$ algebra. The algebra $A_{n}(0,b,-b^2)$ is a coset of the braid algebra. The two other algebras $B_{n}$ and $C_{n}$ do not possess any parameter, and can be also viewed as a coset of the braid algebra. |
| title | Back to baxterisation |
| topic | Mathematical Physics Quantum Algebra |
| url | https://arxiv.org/abs/1708.02754 |