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What is the $L$-module structure on $V\otimes W$ where $L$ is a Lie-algebra and $V,W$ are $L$-modules?

The following question is related but I can't find the definition in there: tensor product of modules of Lie algebras

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    look here: https://en.wikipedia.org/wiki/Lie_algebra_representation – James S. Cook Oct 18 '15 at 17:32
  • Thanks, that's exactly what i needed: $x(v\otimes w)=(xv)\otimes w+v\otimes(xw)$ – inclusive Oct 18 '15 at 18:17
  • Glad to help, I think usually the answer to such questions is something along the lines of: it's the only formula which makes sense given the circumstances. – James S. Cook Oct 18 '15 at 19:42
  • @James: that seems totally unhelpful. For example, you might have guessed that it was $x(v \otimes w) = (xv) \otimes (xw)$, like it is for groups. There's something to explain here. – Qiaochu Yuan Oct 18 '15 at 22:12
  • @QiaochuYuan fair enough (in this case), but, I think it is not unreasonable to suggest that in many such situations it is enough to write what can be written. – James S. Cook Oct 19 '15 at 18:57

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