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A Lie λ-differential algebra is a Lie algebra L with a linear operator D : L → L satisfying the differential relation

$D([xy]) = [D(x)y] + [xD(y)] + λ[D(x)D(y)], x, y ∈ L. $

How derivation map can be defined on Lie λ-differential algebra?

Nil
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  • Could you give more context? e.g. what you mean with "derivation map on Lie $\lambda$-differential algebra", or what makes you suspect that it can be defined/what for you need to know this. – student91 Feb 28 '23 at 12:26
  • By derivation, I mean: for Lie algebra L which we have $D: L \to L$ satisfying D[x,y]=[D(x),y] + [x,D(y)]. Is it possible to define a dertivation map like Lie algebras? – Nil Feb 28 '23 at 15:02
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    You can define a derivation for any Lie algebra. Here you should distinguish between the special operator $D$ and other derivations $d$, where you just view your algebra as a Lie algebra. Do you have a reference for such algebras? I only found this article. – Dietrich Burde Mar 05 '23 at 09:53
  • @DietrichBurde, I could not find any reference for that. Thank you for sharing the reference. I understood. – Nil Mar 05 '23 at 14:50

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