The concepts of derivation and centroid for Lie–Yamaguti algebras are generalized in this paper. A quasi-derivation a LY-algebra can be embedded as larger LY-algebra. relationship between quasi-derivations robustness has been studied.

Let  be a Banach algebra. Let  be linear mappings on . First we demonstrate a theorem concerning the continuity of double derivations; especially that all of -double derivations are continuous on semi-simple Banach algebras, in certain case. Afterwards we define a new vocabulary called “-higher double derivation” and present a relation between this subject and derivations and finally give some ...

Let H be a finitely-generated free abelian group and L(H) the graded free Lie algebra on H . There is a natural homomorphism H ⊗ L(H)→ L(H) defined by bracketing, whose kernel is denoted D(H). If H supports a non-singular symplectic form, eg H = H1(Σ), where Σ is a closed orientable surface, with symplectic basis {xi, yi}, then D(H) is, in fact, a Lie algebra. It can be identified with the Lie ...

let  be a banach algebra. let  be linear mappings on . first we demonstrate a theorem concerning the continuity of double derivations; especially that all of -double derivations are continuous on semi-simple banach algebras, in certain case. afterwards we define a new vocabulary called “-higher double derivation” and present a relation between this subject and derivations and finally give some ...

Let A be a unital algebra and M be a unital A-bimodule. A characterization of generalized derivations and generalized Jordan derivations from A into M, through zero products or zero Jordan products, is given. Suppose that M is a unital left A-module. It is investigated when a linear mapping from A into M is a Jordan left derivation under certain conditions. It is also studied whether an algebra...