%0 Journal Article
%T Back to Baxterisation
%+ Laboratoire Charles Coulomb (L2C)
%+ Laboratoire d'Annecy-le-Vieux de Physique Théorique (LAPTH)
%A Crampé, Nicolas
%A Ragoucy, E.
%A Vanicat, M.
%< avec comité de lecture
%J Commun.Math.Phys.
%V 365
%N 3
%P 1079-1090
%8 2019
%D 2019
%R 10.1007/s00220-019-03299-6
%Z Physics [physics]/Mathematical Physics [math-ph]Journal articles
%X 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.
%G English
%L hal-02065989
%U https://hal.science/hal-02065989
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%~ MIPS
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%~ UM-2015-2021