# lie algebra homomorphismの例文

もっと例文: 1 2

- 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*. - The map \ mathfrak g \ to \ Gamma ( TM ), X \ mapsto X ^ \ # can then be shown to be a
*Lie algebra homomorphism*. - If is such a representation, then according to the relation between Lie groups and Lie algebras, it induces a Lie algebra representation, i . e ., a
*Lie algebra homomorphism* from or to the Lie algebra of commutator bracket. - The corresponding
*Lie algebra homomorphism* \ mathfrak { g } \ to \ mathfrak { gl } ( \ mathfrak { g } ) is called the adjoint representation of \ mathfrak { g } and is denoted by \ operatorname { ad }. - The second requirement for the " G "-action to be Hamiltonian is that the map \ xi \ mapsto H _ \ xi be a
*Lie algebra homomorphism* from \ mathfrak { g } to the algebra of smooth functions on " M " under the Poisson bracket.