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# lie group homomorphism in a sentence

1. It follows immediately that if is simply connected, then the Lie algebra functor establishes a bijective correspondence between Lie group homomorphisms and Lie algebra homomorphisms.
2. Two Lie groups are called " isomorphic " if there exists a bijective homomorphism between them whose inverse is also a Lie group homomorphism.
3. If " H " is a Lie group, then any Lie group homomorphism f : G \ to H is uniquely determined by its differential df.
4. Let G act on a symplectic manifold ( M, \ omega ) with \ Phi _ G : M \ rightarrow \ mathfrak { g } ^ * a moment map for the action, and \ psi : H \ rightarrow G be a Lie group homomorphism, inducing an action of H on M.
5. Let " G " be the subgroup of GL _ n ( \ mathbb { R } ) generated by e ^ { \ mathfrak { g } } and let \ widetilde { G } be a simply connected covering of " G "; it is not hard to show that \ widetilde { G } is a Lie group and that the covering map is a Lie group homomorphism.
6. It's difficult to find lie group homomorphism in a sentence.

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