Shephard-Todd-Chevalley Theorem for skew polynomial rings

Details Shephard-Todd-Chevalley Theorem for skew polynomial rings Shephard-Todd-Chevalley Theorem for skew polynomial rings

2008-06-19

arxiv.org/abs/0806.3210v1

Mathematics

Rings and Algebras

31 pages

Scientific paper

We prove the following generalization of the classical Shephard-Todd-Chevalley Theorem. Let $G$ be a finite group of graded algebra automorphisms of a skew polynomial ring $A:=k_{p_{ij}}[x_1,...,x_n]$. Then the fixed subring $A^G$ has finite global dimension if and only if $G$ is generated by quasi-reflections. In this case the fixed subring $A^G$ is isomorphic a skew polynomial ring with possibly different $p_{ij}$'s. A version of the theorem is proved also for abelian groups acting on general quantum polynomial rings.

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