3-Lie algebras, ternary Nambu-Lie algebras and the Yang-Baxter equation

We construct ternary self-distributive (TSD) objects from compositions of binary Lie algebras, 3-Lie algebras and, in particular, Nambu-Lie algebras. show that the structures obtained satisfy an invertibility property resembling racks. prove these give rise to Yang-Baxter operators tensor product base vector space upon defining suitable twisting isomorphisms, we obtain representations infinite (framed) braid group. consider examples for low-dimensional where bracket is defined by composition ones, along with simple are not gauge equivalent transposition operator, and problem deforming new solutions equation. discuss applications this deformation procedure construction link invariants.