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arXiv · 1107.4420

Generalized δ-Derivations

Ivan Kaygorodov
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Abstract

We defined generalized δ-derivations of algebra A as linear mapping χassociated with usual δ-derivation ϕby the rule χ(xy)=δ(χ(x)y+xϕ(y))=δ(ϕ(x)y+xχ(y)) for any x,y \in 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 < >, 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.

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Ivan Kaygorodov. 2011-07-22. Generalized δ-Derivations. https://arxiv.org/abs/1107.4420

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