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Invariant fields of finite irreducible reflection groups (1999)

Kemper, Gregor ; Malle, Gunter

Springer

Mathematische Annalen 315 (1999), S. 569-586

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ISSN: 1432-1807

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract. We prove the following result: If G is a finite irreducible reflection group defined over a base field k, then the invariant field of G is purely transcendental over k, even if |G| is divisible by the characteristic of k. It is well known that in the above situation the invariant ring is in general not a polynomial ring. So the question whether at least the invariant field is purely transcendental (Noether's problem) is quite natural.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/s002080050329

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