Timeline for Name/terminology for a relationship between group actions

7 events

when toggle format	what		by	license	comment
Jul 21, 2014 at 17:49	comment	added	Lee Mosher		How about "$\phi$ is action preserving"? Or "$\phi$ is an action homomorphism"? Underlying this is the observation that $\phi$ is a morphism in a category of group actions on $X$.
Jul 15, 2014 at 8:39	comment	added	user43326		I would say that the identity map of $X$ is equivariant with respect to the two action of $G$.
Jul 14, 2014 at 21:22	comment	added	Geoff Robinson		It is more usually used for modules. If $N \lhd G$ and $G/N$ acts on some structure, "inflation" to an action of $G$ is just the process of making $G$ act on the same structure by letting $N$ acts trivially, and letting $g$ act as the coset $gN$ did for each $g \in G$ - the point being that this action is well-defined.
Jul 14, 2014 at 21:06	comment	added	Iian Smythe		What is the definition of "inflation" here?
Jul 14, 2014 at 20:51	comment	added	Geoff Robinson		Note that ${\rm ker} \phi$ acts trivially on $X.$ Hence the $G$-set $X$ is the inflation of $X$ as ${\rm Im} \phi$-set.
Jul 14, 2014 at 20:29	history	edited	Iian Smythe		edited tags
Jul 14, 2014 at 20:24	history	asked	Iian Smythe	CC BY-SA 3.0