lie groups and lie algebrasの例文


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  1. A large number of modern mathematical theories harmoniously converges in the framework of secondary calculus, for instance : commutative algebra and algebraic geometry, homological algebra and differential topology, Lie group and Lie algebra theory, differential geometry, etc.
  2. 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.
  3. The groups that describe those symmetries are Lie groups, and the study of Lie groups and Lie algebras reveals much about the physical system; for instance, the number of force carriers in a theory is equal to dimension of the Lie algebra, and these bosons interact with the force they mediate if the Lie algebra is nonabelian.
  4. The use of Grassmann-valued coordinates has spawned the field of supermathematics, wherein large portions of geometry can be generalized to super-equivalents, including much of Riemannian geometry and most of the theory of Lie groups and Lie algebras ( such as Lie superalgebras, " etc . " ) However, issues remain, including the proper extension of deRham cohomology to supermanifolds.


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