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- W2062327241 abstract "Let G⊂GL(V) be a finite group, where V is a finite dimensional vector space over a field F of arbitrary characteristic. Let S(V) be the symmetric algebra of V and S(V)G the ring of G-invariants. We prove here the following results: TheoremSuppose that G contains no pseudo-reflection (of any kind).(1)If S(V)G is Gorenstein, then G⊂SL(V).(2)If G⊂SL(V) then the Cohen–Macaulay locus of S(V)G coincides with its Gorenstein locus. In particular if S(V)G is Cohen–Macaulay then it is also Gorenstein. Theorem Suppose that G contains no pseudo-reflection (of any kind). If S(V)G is Gorenstein, then G⊂SL(V). If G⊂SL(V) then the Cohen–Macaulay locus of S(V)G coincides with its Gorenstein locus. In particular if S(V)G is Cohen–Macaulay then it is also Gorenstein. This extends well-known results of K. Watanabe in case (charF,|G|)=1. It also confirms a special case of a conjecture due to G. Kemper, E. Körding, G. Malle, B.H. Matzat, D. Vogel and G. Wiese. A similar extension is given to D. Bensonʼs theorem about the Gorenstein property of (S(V)⊗Λ(V))G, the polynomial tensor exterior algebra invariants. Our proof uses non-commutative algebra methods in an essential way." @default.
- W2062327241 created "2016-06-24" @default.
- W2062327241 creator A5011853218 @default.
- W2062327241 date "2011-11-01" @default.
- W2062327241 modified "2023-09-29" @default.
- W2062327241 title "On the Gorenstein property for modular invariants" @default.
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- W2062327241 doi "https://doi.org/10.1016/j.jalgebra.2011.07.030" @default.
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