- #1
mnb96
- 715
- 5
Hello,
in group theory a regular action on a G-set S is such that for every x,y∈S, there exists exactly one g such that g⋅x = y.
I noticed however that in the theory of Lie groups the definition of regular action is quite different (see Definition 1.4.8 at this link).
Is there a connection between the two definition? I would like to understand why a regular Lie group action is defined in that way.
Thanks.
in group theory a regular action on a G-set S is such that for every x,y∈S, there exists exactly one g such that g⋅x = y.
I noticed however that in the theory of Lie groups the definition of regular action is quite different (see Definition 1.4.8 at this link).
Is there a connection between the two definition? I would like to understand why a regular Lie group action is defined in that way.
Thanks.