The Noether Map I
-
Mara D. Neusel
Abstract
Let æ : G ↪ GL(n, 𝔽) be a faithful representation of a finite group G. In this paper we study the image of the associated Noether map
.
It turns out that the image of the Noether map characterizes the ring of invariants in the sense that its integral closure 
. This is true without any restrictions on the group, representation, or ground field. Moreover, we show that the extension 
is a finite p-root extension if the characteristic of the ground field is p. Furthermore, we show that the Noether map is surjective, if V = 𝔽n is a projective 𝔽G-module. We apply these results and obtain upper bounds on the degrees of a minimal generating set of 𝔽[V]G and the Cohen-Macaulay defect of 𝔽[V]G. We illustrate our results with several examples.
© de Gruyter 2009
Articles in the same Issue
- The Noether Map I
- A general notion of algebraic entropy and the rank-entropy
- Computing the maximal algebra of quotients of a Lie algebra
- Mahler measure under variations of the base group
- Extremal α-pseudocompact abelian groups
- Group algebras whose symmetric and skew elements are Lie solvable
- Walks on graphs and lattices – effective bounds and applications
- Strichartz and smoothing estimates for Schrödinger operators with almost critical magnetic potentials in three and higher dimensions
- On the homotopy type of the non-completed classifying space of a p-local finite group
Articles in the same Issue
- The Noether Map I
- A general notion of algebraic entropy and the rank-entropy
- Computing the maximal algebra of quotients of a Lie algebra
- Mahler measure under variations of the base group
- Extremal α-pseudocompact abelian groups
- Group algebras whose symmetric and skew elements are Lie solvable
- Walks on graphs and lattices – effective bounds and applications
- Strichartz and smoothing estimates for Schrödinger operators with almost critical magnetic potentials in three and higher dimensions
- On the homotopy type of the non-completed classifying space of a p-local finite group
