Hilbert-Weyl theorem
Theorem: Let be a compact Lie group acting on . Then there exists a finite Hilbert basis for the ring (the set of invariant polynomials). [GSS]
proof:
In [GSS] on page 54.
Theorem:(as stated by Hermann Weyl)
The (absolute) invariants corresponding to a given set of representations of a finite or a compact Lie group have a finite integrity basis. [HW]
proof:
In [HW] on page 274.
References
- GSS Golubitsky, Martin. Stewart, Ian. Schaeffer, G. David.: Singularities and Groups in Bifurcation Theory (Volume II). Springer-Verlag, New York, 1988.
- HW Hermann, Weyl: The Classical Groups: Their Invariants and Representations. Princeton University Press, New Jersey, 1946.
| Title | Hilbert-Weyl theorem |
|---|---|
| Canonical name | HilbertWeylTheorem |
| Date of creation | 2013-03-22 13:39:54 |
| Last modified on | 2013-03-22 13:39:54 |
| Owner | mathcam (2727) |
| Last modified by | mathcam (2727) |
| Numerical id | 9 |
| Author | mathcam (2727) |
| Entry type | Theorem |
| Classification | msc 22E20 |