Applications of Lie Groups to Differential Equations¶
Olver, P. J. (1986). Applications of Lie Groups to Differential Equations. Springer-Verlag.
Cited by¶
2 citations across 2 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Equivariance
- Mathematics: Equivariant maps between G-sets and G-spaces; intertwining operators in representation theory; natural transformations in category theory (a naturality square is a commuting diagram of the same shape); equivariant cohomology and equivariant K-theory, where the group action is carried through every construction; Noether's theorem, which ties continuous symmetries of a system to conserved quantities and rests on the covariance of the action functional, a connection Olver (1986) develops systematically through the theory of symmetry groups of differential equations.
This sourceSystematic theory of symmetry groups of differential equations; Noether's theorem linking continuous symmetries to conservation laws, plus the symmetry-reduction method (solve on a representative, transport across the group).
- Mathematics: Equivariant maps between G-sets and G-spaces; intertwining operators in representation theory; natural transformations in category theory (a naturality square is a commuting diagram of the same shape); equivariant cohomology and equivariant K-theory, where the group action is carried through every construction; Noether's theorem, which ties continuous symmetries of a system to conserved quantities and rests on the covariance of the action functional, a connection Olver (1986) develops systematically through the theory of symmetry groups of differential equations.
- Noether's Theorem
- Modern expositions by Marsden-Ratiu (1994) frame Noether's theorem in symplectic-geometric language, revealing its natural home in differential geometry; Olver (1986)
This sourceSystematic theory of symmetry groups of differential equations; develops Noether's theorem linking continuous symmetries to conservation laws via covariance of the action functional, and the symmetry-reduction method of solving on a representative and transporting across the group.
- Modern expositions by Marsden-Ratiu (1994) frame Noether's theorem in symplectic-geometric language, revealing its natural home in differential geometry; Olver (1986)
Verification¶
This reference passed the adversarial substantiation pipeline: it was checked to exist and to support the claim it is attached to. See how references were verified.
Registry ID ref:855f72b98e0d · see in the full table