Shephard–Todd–Chevalley Theorem for Skew Polynomial Rings

By E. Kirkman, James Kuzmanovich, James J. Zhang. 2008

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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 $A:=k_{p_{ij}}[x_1,\cdots,x_n]$. Then the fixed subring AG has finite global dimension if and only if G is generated by quasi-reflections. In this case the fixed subring AG is isomorphic to a skew polynomial ring with possibly different pij’s. A version of the theorem is proved also for abelian groups acting on general quantum polynomial rings.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ad41ec12f1e52487627ad6cbb74933d78de4fd97