Generalized δ-Derivations
Abstract
We defined generalized δ-derivations of algebra A as linear mapping associated with usual δ-derivation φ by the rule (xy)=δ((x)y+xφ(y))=δ(φ(x)y+x(y)) for any x,y ∈ A. We described generalized δ-derivations of prime alternative algebras, prime Lie algebras and superalgebras, unital algebras, and semisimple finite-dimensional Jordan superalgebras. In this cases we proved that generalized δ-derivation is a generalized derivation or δ-derivation. After that we described δ-superderivations of superalgebras <<KKM Double>>, arising from prime alternative algebras, prime Lie algebras and superalgebras, unital algebras, and semisimple finite-dimensional Jordan superalgebras. In the end, we constructed new examples of non-trivial δ-derivations of Lie algebras.
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.