# lie group homomorphism in a sentence

- 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. - Two Lie groups are called " isomorphic " if there exists a bijective homomorphism between them whose inverse is also a
*Lie group homomorphism*. - If " H " is a Lie group, then any
*Lie group homomorphism* f : G \ to H is uniquely determined by its differential df. - 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. - 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*. - It's difficult to find
*lie group homomorphism* in a sentence.