Cartier, Pierre 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 Sémin. Lothar. Comb. 23, B23a, 28 p. (1990). 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 PDFBibTeX XMLCite \textit{P. Cartier}, Sémin. Lothar. Comb. 23, B23a, 28 p. (1990; Zbl 1060.82505) Full Text: EuDML EMIS