α, β)-derivations associated to LY-algebras

Abstract

LY-algebras (Lie-Yamaguti algebras) have been widely studied in recent times due to their special nature of satisfying both the bilinear and trilinear operations simultaneously. Various research have been made on LY-algebras related to their representations, cohomologies, deformations, extensions, irre-ducibility and other structural properties. In this study, the (α, β)-derivations of LY-algebras are discussed. Taking α and β as automorphisms of an LY-algebra, the concept of (α, β)-derivations, which are derivations under both the bilinear and trilinear operations is defined for LY-algebras. Then some of their important properties are studied along with their relationship with other generalized derivations of LY-algebras.