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).
Supported in partVerified against the publisher's abstract
Olver's abstract covers symmetry groups of differential equations and their connection to conservation laws, but not the covariance of the action functional.
“the connections between conservation laws and symmetry groups”
- 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¶
Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.
Does it back the claim? Read against the text for 1 of 2 citations: 1 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.
Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.
See how references were verified.
Registry ID ref:855f72b98e0d · see in the full table