# lie groups and lie algebrasの例文

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- 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. - 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 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. - 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.