Back to Baxterisation

  • N. Crampe
  • E. Ragoucy
  • M. VanicatEmail author


In the continuity of our previous paper (Crampe et al. in Commun Math Phys 349:271, 2017, arXiv:1509.05516), we define three new algebras, \({\mathcal{A}_{\mathfrak{n}}(a,b,c)}\), \({\mathcal{B}_{\mathfrak{n}}}\) and \({\mathcal{C}_{\mathfrak{n}}}\), that are close to the braid algebra. They allow to build solutions to the 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 \({\mathcal{A}_{\mathfrak{n}}(a,b,c)}\) algebra depends on three arbitrary parameters, and when the parameter a is set to zero, we recover the algebra \({\mathcal{M}_{\mathfrak{n}}(b,c)}\) already introduced elsewhere for purpose of baxterisation. The Hecke algebra (and its baxterisation) can be recovered from a coset of the \({\mathcal{A}_{\mathfrak{n}}(0,0,c)}\) algebra. The algebra \({\mathcal{A}_{\mathfrak{n}}(0,b,-b^2)}\) is a coset of the braid algebra. The two other algebras \({\mathcal{B}_{\mathfrak{n}}}\) and \({\mathcal{C}_{\mathfrak{n}}}\) do not possess any parameter, and can be also viewed as a coset of the braid algebra.


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Authors and Affiliations

  1. 1.Laboratoire Charles Coulomb (L2C)UMR 5221 CNRS-Université de MontpellierMontpellierFrance
  2. 2.Laboratoire de Physique Théorique LAPThCNRS and Université Savoie Mont BlancAnnecy-le-Vieux CedexFrance

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