Projects per year
Abstract
Given a settheoretic solution (X, r) of the YangBaxter equation, we denote by M = M(X, r) the structure monoid and by A = A(X, r), respectively A0 = A0 (X, r), the left, respectively right, derived structure monoid of (X, r). It is shown that there exist a left action of M on A and a right action of M on A0 and 1cocycles π and π 0 of M with coefficients in A and in A0 with respect to these actions, respectively. We investigate when the 1cocycles are injective, surjective, or bijective. In case X is finite, it turns out that π is bijective if and only if (X, r) is left nondegenerate, and π 0 is bijective if and only if (X, r) is right nondegenerate. In case (X, r) is left nondegenerate, in particular π is bijective, we define a semitruss structure on M(X, r) and then we show that this naturally induces a settheoretic solution (M, r) on the least cancellative image M = M(X, r)/η of M(X, r). In case X is naturally embedded in M(X, r)/η, for example when (X, r) is irretractable, then r is an extension of r. It is also shown that nondegenerate irretractable solutions necessarily are bijective.
Original language  Catalan 

Pages (fromto)  0499528 
Number of pages  30 
Journal  Publicacions matemàtiques 
Volume  65 
Issue number  2 
Publication status  Published  2021 
Keywords
 Yangbaxter equation
 Settheoretic solution
 Structure monoid
 1cocycle
 Semitruss
Projects
 1 Finished

Estructura y clasificación de anillos, módulos y c*algebras: interacciones con dinámica, combinatoria y topología
Ara Bertran, P., Dicks Mclay, W., Antoine Riolobos, R., Cedo Gine, F., Herbera Espinal, D., Perera Domenech, F., Bosa Puigredon, J., Cantier, L. N., Claramunt Carós, J., Jespers, E. F., Okninski, J., Sánchez Serdà, J., Pardo Espino, E. & Vilalta Vila, E.
1/01/18 → 30/09/21
Project: Research Projects and Other Grants