环上群作用的模块结构

Selecta Mathematica Pub Date : 2024-08-29 DOI:10.1007/s00029-024-00968-w

Peter Symonds

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摘要

考虑一个有限群 G 作用于有级 Noetherian k-algebra S，对于某个特征 p 的域 k；例如，S 可能是一个多项式环。把 S 看作一个 kG 模块，并考虑特定不可分解模块作为各阶和的多重性。我们将展示如何用同调代数来描述这一点，以及如何将其与 S 的谱上的群作用几何联系起来。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The module structure of a group action on a ring

Consider a finite group G acting on a graded Noetherian k-algebra S, for some field k of characteristic p; for example S might be a polynomial ring. Regard S as a kG-module and consider the multiplicity of a particular indecomposable module as a summand in each degree. We show how this can be described in terms of homological algebra and how it is linked to the geometry of the group action on the spectrum of S.

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Selecta Mathematica

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