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Baxterization. (English) Zbl 0744.57005

“Baxterization” is the author’s term for the procedure of inserting a spectral parameter into a coherent sequence of representations of the braid group \(B_ n\) so that the Yang-Baxter equations (YBE) are satisfied and so that the original braid group representations are the infinite limit in the spectral limit of the Baxterized version. This article sketches the origin of the YBE in statistical mechanics, describes briefly braids, braid groups, knots and links and gives examples of Baxterization (corresponding to the Hecke and Birman- Murakumi-Wenzl algebras). It concludes with the suggestion that the YBE should be considered as more natural than the braid equations, and gives some further evidence.

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
20F36 Braid groups; Artin groups
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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