# What does “lifted action” mean?

I read about angular moment and linear moment but I don't know what "lifted action" means. Can you explain please?

Thanks. :)

-
With the current information, I think Alexander Gruber's answer is very good, but I'm curious to see more context of your question (concerning angular moment and linear moment) in case there's anything else to be said. – rschwieb Mar 14 '13 at 13:34
@rschwieb For what it's worth, me too. There seems like there's something pretty cool behind this, but I can only answer the question I'm given. – Alexander Gruber Mar 14 '13 at 16:23

If you have a subgroup $\overline{M}$ of a quotient group $G/N$, the lift of $\overline{M}$ is a subgroup $M$ of $G$ such that the $\overline{M}$ is the image of $M$ under the projection homomorphism $G\rightarrow G/N$. (This is guaranteed to exist by the correspondence theorem.) So speaking of the lifted action of some group action implies that you are working with an element (or subgroup) of a factor group and you need to find the preimage of said element (or subgroup) in $G$.
An example of this is that if $G$ acts on an object $X$ ($X$ could be a group, a tree, a vector space, a whatever you want) then there is some homomorphism $\phi: G\rightarrow \operatorname{Aut}(X)$. If $\phi$ has non-trivial kernel then the action of $\operatorname{im}(\phi)$ lifts to an action of $G$. (I suppose it will always lift, but if the kernel is trivial then the lift is boring (aka trivial).) – user1729 Mar 14 '13 at 16:06