A Brief Guide to Cabling and Endocabling.

Abstract: Cabling is a method developed by Lebed, Ramìrez and Vendramin to deform involutive, non-degenerate solutions to the Yang-Baxter equations while keeping control over the diagonal maps of the resulting solutions. This powerful tool allows one to prove a plethora of decomposability results for involutive solutions and has recently been generalized by Colazzo and Van Antwerpen to obtain similar results for non-involutive solutions. In this talk, I will give an outline of classical cabling in the style of Lebed, Ramìrez and Vendramin, and explain some standard applications of the method. Afterwards, I will demonstrate how classical cabling can be generalized to endocabling, where involutive solutions are deformed by means of endomorphisms of the module structure of permutation braces which is given by the λ-action. Finally, I will give a rough sketch how endocabling can be applied to provide insights into the structure of solutions whose diagonal map is a cyclic permutation.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar