Hilbert-Weyl theorem

Theorem:Let $\\Gamma$ be a compact Lie group acting on $V$ . Then there exists a finite Hilbert basis for the ring $\\mathcal{P}(\\Gamma)$ (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.

单词	HilbertWeylTheorem
释义	Hilbert-Weyl theorem Theorem:Let $\\Gamma$ be a compact Lie group acting on $V$ . Then there exists a finite Hilbert basis for the ring $\\mathcal{P}(\\Gamma)$ (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.
随便看	Poisson ring PoissonsEquation PoissonSummationFormula Poisson summation formula Poisson’s equation Poker poker PolarCoordinates polar coordinates PolarCurve polar curve PolarDecomposition polar decomposition PolarDecompositionInVonNeumannAlgebras polar decomposition in von Neumann algebras PolaritiesAndForms polarities and forms Polarity polarity PolarizationByDifferentialOperators polarization by differential operators PolarizationIdentity polarization identity PolarSet polar set