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New adventures in the land of \(q\)-analogues (Yang-Baxter equations). (Nouvelles aventures au pays des \(q\)-analogues (équation de Yang-Baxter).) (French) Zbl 1060.82505

Summary: The purpose of this paper is to give an introduction to the methods of Statistical Mechanics, to derive the relations between the Yang-Baxter equation, the Hecke algebra and the braid group. The underlying \(q\)-calculus involves an algebra of noncommutative polynomials in two variables \(x, y\) such that \(yx=qxy\).

MSC:

82B23 Exactly solvable models; Bethe ansatz
17B37 Quantum groups (quantized enveloping algebras) and related deformations
20C08 Hecke algebras and their representations
20F36 Braid groups; Artin groups
05A30 \(q\)-calculus and related topics
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