3-Lie Algebras, Ternary Nambu-Lie algebras and link invariants

We construct ternary self-distributive (TSD) objects from compositions of binary Lie algebras, $3$-Lie algebras and, in particular, ternary Nambu-Lie algebras. We show that the structures obtained satisfy an invertibility property resembling that of racks. We prove that these structures give rise to Yang-Baxter operators in the tensor product of the base vector space and, upon defining suitable twisting isomorphisms, we obtain representations of the infinite (framed) braid group. We use these results to construct invariants of (framed) links. We consider examples for low-dimensional Lie algebras, where the ternary bracket is defined by composition of the binary ones, along with simple $3$-Lie algebras, and their applications to some classes of links.