German Garcia: Generalizations of derivations and n-hom-Lie algebras

Abstract: In this talk I will introduce a generalization of n-hom-Lie algebras based on previous work with Jacobian hom-algebras. The Jacobi-type identity is asymmetrical, which leads to reexamining the axiom “the adjoint is a hom-derivation” that characterizes hom-Lie algebras, and to some extent their n-ary counterpart. I will introduce bi-generalized derivations as an approach to this problem and establish a relationship between them and the adjoint multiplication maps and introduce two types of extensions, one based on bi-generalized derivations and one based on generalized trace operators.