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lie algebra homomorphismの例文

例文

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  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. The map \ mathfrak g \ to \ Gamma ( TM ), X \ mapsto X ^ \ # can then be shown to be a Lie algebra homomorphism.
  3. 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.
  4. 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 }.
  5. 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.

隣接する単語

  1. "lie algebra action"の例文
  2. "lie algebra bundle"の例文
  3. "lie algebra bundles"の例文
  4. "lie algebra cohomology"の例文
  5. "lie algebra extension"の例文
  6. "lie algebra of a lie group"の例文
  7. "lie algebra representation"の例文
  8. "lie algebras"の例文
  9. "lie algebroid"の例文
  10. "lie along"の例文
  11. "lie algebra cohomology"の例文
  12. "lie algebra extension"の例文
  13. "lie algebra of a lie group"の例文
  14. "lie algebra representation"の例文
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