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it is known that "EveryregularG-action is isomorphic to the action of G on G given by left multiplication".

Is this true also when G is aLie 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 It says: "The above statements about isomorphisms for regular, free and transitive actions are no longer valid for continuous group actions.".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.

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# Question on Lie group regular actions

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