A characterization of linearly reductive groups by their invariants

G. Kemper

doi:10.1007/BF01237180

A characterization of linearly reductive groups by their invariants

G. Kemper

Heidelberg University

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

The theorem of Hochster and Roberts says that, for every module V of a linearly reductive group G over a field K, the invariant ring K[V]^G is Cohen-Macaulay. We prove the following converse: if G is a reductive group and K[V]^G is Cohen-Macaulay for every module V, then G is linearly reductive.

Original language	English
Pages (from-to)	85-92
Number of pages	8
Journal	Transformation Groups
Volume	5
Issue number	1
DOIs	https://doi.org/10.1007/BF01237180
State	Published - 2000
Externally published	Yes

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abstract = "The theorem of Hochster and Roberts says that, for every module V of a linearly reductive group G over a field K, the invariant ring K[V]G is Cohen-Macaulay. We prove the following converse: if G is a reductive group and K[V]G is Cohen-Macaulay for every module V, then G is linearly reductive.",

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AB - The theorem of Hochster and Roberts says that, for every module V of a linearly reductive group G over a field K, the invariant ring K[V]G is Cohen-Macaulay. We prove the following converse: if G is a reductive group and K[V]G is Cohen-Macaulay for every module V, then G is linearly reductive.

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A characterization of linearly reductive groups by their invariants

Abstract

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