Shephard-Todd-Chevalley Theorem for skew polynomial rings

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dc.creatorKirkman, E.
dc.creatorKuzmanovich, J.
dc.creatorZhang, J. J.
dc.date2008-06-19
dc.date.accessioned2026-07-07T09:45:36Z
dc.date.available2026-07-07T09:45:36Z
dc.descriptionWe 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.
dc.description31 pages
dc.identifierhttps://arxiv.org/abs/0806.3210
dc.identifierhttp://arxiv.org/abs/0806.3210
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/163249
dc.subjectRings and Algebras
dc.subject16A62; 16E70; 20J50
dc.titleShephard-Todd-Chevalley Theorem for skew polynomial rings
dc.typetext

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