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- Image of Homomorphism of Lie groups 1 answer
Is a conjugation of a Lie subgroup a Lie subgroup?
- Conjugation of a subgroup is a subgroup. Thus, a conjugation of a Lie subgroup is a subgroup.
- Conjugation is a diffeomorphism. Thus, a conjugation of a Lie subgroup is the image of a manifold by a diffeomorphism, and so it is an embedded submanifold.
- Finally I need to prove the smoothness of the group multiplication and inverse operation. But I'm not sure that the restrictions of them on the submanifold are still smooth. How can I prove this?