Invariant Theory of Finite Groups

More documents

Recommendations

Info

Invariant Theory of Finite Groups – p. 23/2Remarks on Noether’s theoremSuppose |G| ∈ F ∗ . Then the transfer maptr : A → A G ,a ↦→ ∑ g∈Gg(a)is a surjective homomorphism of A G - modules.A = 〈x b 11 x b 22 ...x b dd| b i < max(2, |G|)〉 B . ⇒A G = 〈tr(x b 11 x b 22 ...x b dd) | b i < max(2, |G|), ∑ b i > 0〉 B ⇒A G = F[B, tr(x b 11 x b 22 ...x b dd) | b i < max(2, |G|) ] ⇒A G can be generated in degrees ≤ max{|G|,d · (|G| − 1)}.
Invariant Theory of Finite Groups – p. 24/2Constructive AspectsDefinition: (Degree bounds, Noether - number)β(A G ) := min{k | A G generated in degree ≤ k} < ∞
Page 1 and 2: Invariant Theory of Finite Groups -
Page 6 and 7: Geometric BackgroundAlgebraic Geome
Page 18 and 19: ExamplesSymmetric polynomials:G :=

Invariant Theory of Finite Groups

Create successful ePaper yourself

Delete template?

Save as template?