Details:
Title  Homomorphisms, localizations and a new algorithm to construct invariant rings of finite groups  Author(s)  Peter Fleischmann, Gregor Kemper, Chris Woodcock  Type  Article in Journal  Abstract  Let G be a finite group acting on a polynomial ring A over the field K and let A G denote the corresponding ring of invariants. Let B be the subalgebra of A G generated by all homogeneous elements of degree less than or equal to the group order  G  . Then in general B is not equal to A G if the characteristic of K divides  G  . However we prove that the field of fractions Quot ( B ) coincides with the field of invariants Quot ( A G ) = Quot ( A ) G . We also study various localizations and homomorphisms of modular invariant rings as tools to construct generators for A G . We prove that there is always a nonzero transfer c ∈ A G of degree <  G  , such that the localization ( A G ) c can be generated by fractions of homogeneous invariants of degrees less than 2 ⋅  G  − 1 . If A = Sym ( V ⊕ F G ) with finitedimensional F G module V, then c can be chosen in degree one and 2 ⋅  G  − 1 can be replaced by  G  . Let N denote the image of the classical Noetherhomomorphism (see the definition in the paper). We prove that N contains the transfer ideal and thus can be used to calculate generators for A G by standard elimination techniques using Gröbnerbases. This provides a new construction algorithm for A G .  Keywords  Modular invariant theory, Computational algebra, Localization  ISSN  00218693 
URL 
http://www.sciencedirect.com/science/article/pii/S0021869305006435 
Language  English  Journal  Journal of Algebra  Volume  309  Number  2  Pages  497  517  Year  2007  Note  Computational Algebra  Edition  0  Translation 
No  Refereed 
No 
