Register to reply 
Question on Lie group regular actions 
Share this thread: 
#1
Jan2713, 04:35 PM

P: 625

Hello,
it is known that "Every regular Gaction is isomorphic to the action of G on G given by left multiplication". Is this true also when G is a Lie group? There is an ambiguous sentence in Wikipedia that is confusing me. It says: "The above statements about isomorphisms for regular, free and transitive actions are no longer valid for continuous group actions.". This sentence probably refers to the above statement about the isomorphism of regular actions and the action of G on itself, but I don't understand why it is supposed to be true for Lie group actions. 


#2
Jan2813, 10:31 AM

Sci Advisor
P: 3,295




#3
Jan2813, 04:09 PM

P: 625

Hi Stephen!
thanks for your reply. You are right! I didn't think that in the context of Lie groups we have to change the definition of isomorphism and impose some constraints of continuity on the mapping. This basically answers my question. 


Register to reply 
Related Discussions  
Question on regular group actions  Linear & Abstract Algebra  0  
Faithful Group Actions  Calculus & Beyond Homework  1  
Question on group actions on vector spaces  Linear & Abstract Algebra  5  
Group actions  Linear & Abstract Algebra  1  
Group actions  Calculus & Beyond Homework  1 