A moment map for the variety of Jordan algebras

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-04 DOI:10.1142/s0219199724500159

Claudio Gorodski, Iryna Kashuba, María Eugenia Martin

引用次数: 0

Abstract

We study the variety of complex $n$ -dimensional Jordan algebras using techniques from Geometric Invariant Theory. More specifically, we use the Kirwan–Ness theorem to construct a Morse-type stratification of the variety of Jordan algebras into finitely many invariant locally closed subsets, with respect to the energy functional associated to the canonical moment map. In particular we obtain a new, cohomology-free proof of the well-known rigidity of semisimple Jordan algebras in the context of the variety of Jordan algebras.

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乔丹代数的矩图

我们利用几何不变论的技术研究了复杂 n 维乔丹代数的种类。更具体地说，我们利用基尔万-内斯（Kirwan-Ness）定理，就与经典矩映射相关的能量函数而言，将乔丹数的种类构造成有限多个不变局部封闭子集的莫尔斯型分层。特别是，我们在乔丹代数的背景下，获得了半简单乔丹代数众所周知的刚性的无同调新证明。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.