The spectrum of a twisted commutative algebra

IF 1.5 1区数学 Q1 MATHEMATICS

Proceedings of the London Mathematical Society Pub Date : 2023-12-22 DOI:10.1112/plms.12576

Andrew Snowden

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引用次数: 0

Abstract

A twisted commutative algebra is (for us) a commutative

Q $\mathbf {Q}$

-algebra equipped with an action of the infinite general linear group. In such algebras, the “

GL $\mathbf {GL}$

-prime” ideals assume the duties fulfilled by prime ideals in ordinary commutative algebra, and so it is crucial to understand them. Unfortunately, distinct

GL $\mathbf {GL}$

-primes can have the same radical, which obstructs one from studying them geometrically. We show that this problem can be eliminated by working with super vector spaces: doing so provides enough geometry to distinguish

GL $\mathbf {GL}$

-primes. This yields an effective method for analyzing

GL $\mathbf {GL}$

-primes.

查看原文本刊更多论文

扭曲交换代数的谱

扭曲交换代数（对我们来说）是一个交换 Q$\mathbf {Q}$-代数，带有无限一般线性群的作用。在这样的代数中，"GL$\mathbf {GL$}-prime" 理想承担着普通交换代数中素数理想的职责，因此理解它们至关重要。遗憾的是，不同的 GL$\mathbf {GL}$-prime 可以具有相同的根，这阻碍了我们从几何学角度对它们进行研究。我们的研究表明，这个问题可以通过超向量空间来解决：超向量空间提供了足够的几何图形来区分 GL$\mathbf {GL}$-primes 。这就产生了分析 GL$\mathbf {GL}$-primes 的有效方法。

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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来源期刊

Proceedings of the London Mathematical Society 数学-数学

CiteScore

2.90

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Proceedings of the London Mathematical Society is the flagship journal of the LMS. It publishes articles of the highest quality and significance across a broad range of mathematics. There are no page length restrictions for submitted papers. The Proceedings has its own Editorial Board separate from that of the Journal, Bulletin and Transactions of the LMS.