R-Matrices, Yetter-Drinfel'd Modules and Yang-Baxter Equation

Victoria Lebed
2013 Axioms  
In the first part we recall two famous sources of solutions to the Yang-Baxter equation-R-matrices and Yetter-Drinfel d (=YD) modules-and an interpretation of the former as a particular case of the latter. We show that this result holds true in the more general case of weak R-matrices, introduced here. In the second part we continue exploring the "braided" aspects of YD module structure, exhibiting a braided system encoding all the axioms from the definition of YD modules. The functoriality and
more » ... e functoriality and several generalizations of this construction are studied using the original machinery of YD systems. As consequences, we get a conceptual interpretation of the tensor product structures for YD modules, and a generalization of the deformation cohomology of YD modules. This homology theory is thus included into the unifying framework of braided homologies, which contains among others Hochschild, Chevalley-Eilenberg, Gerstenhaber-Schack and quandle homologies.
doi:10.3390/axioms2030443 fatcat:a2qgdg4mkfd6zb4aek7wsy2aee