German Garcia: Hom-associative structures, n-hom-Lie algebras, twisted derivations and beyond

Abstract:

In this talk I will present the main results of my PhD thesis. My research tackles mutation algebras from a hom-algebraic standpoint, a graded Lie-type construction based on twisted derivations, zero-division relations linked to hom-associativity, the problem of hom-associative structures and a generalization of n-hom-Lie algebras given by the Jacobian determinant of twisted derivations.