On the Trace of Graded Automorphisms

Jing, Naihuan; Zhang, James J.

doi:10.1006/jabr.1996.6896

Cited by 25 publications

(28 citation statements)

References 9 publications

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“…Since the property of h being a quasi-reflection is determined by T r(h, t) and T r(ghg −1 , t) = T r(h, t) for any g ∈ G, then R is a normal subgroup of G. Thus the quotient group G/R acts on the fixed subring A R , and the fixed subring (A R ) G/R equals A G . Let g ∈ G \ R. Then by [JiZ,Lemma 5…”

Section: Definitionsmentioning

confidence: 98%

Shephard–Todd–Chevalley Theorem for Skew Polynomial Rings

Kirkman

Kuzmanovich

Zhang

2009

Algebr Represent Theor

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Abstract. We prove the following generalization of the classical ShephardTodd-Chevalley Theorem. Let G be a finite group of graded algebra automorphisms of a skew polynomial ring A := kp ij [x 1 , · · · , xn]. Then the fixed subring A G has finite global dimension if and only if G is generated by quasireflections. 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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Section: Definitionsmentioning

confidence: 98%

Shephard–Todd–Chevalley Theorem for Skew Polynomial Rings

Kirkman

Kuzmanovich

Zhang

2009

Algebr Represent Theor

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“…By [JZ1,Theorem 3.1], Tr A (g, t) = 1/p(t) where p(t) is a polynomial of degree 4. We can find p(t) = 1 + a 1 t + a 2 t 2 + a 3 t 3 + a 4 t 4 from the first 5 terms of the trace function Tr(g, t) = 1 + b 1 t + b 2 t 2 + b 3 t 3 + b 4 t 4 + · · · using the standard method of undetermined coefficients to get:…”

Section: Theorem 15 Let G Be a Graded Automorphism Of A Noetherian mentioning

confidence: 98%