Skew-Adjoint Maps and Quadratic Lie Algebras

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-07 DOI:10.1007/s00009-024-02656-7

Pilar Benito, Javier Rández-Ibáñez, Jorge Roldán-López

引用次数: 0

Abstract

The procedure of double extension of vector spaces endowed with non-degenerate bilinear forms allows us to introduce the class of generalized \(\mathbb {K}\)-oscillator algebras over an arbitrary field \(\mathbb {K}\). Starting from basic structural properties and the canonical forms of skew-adjoint endomorphisms, we will proceed to classify the subclass of quadratic nilpotent algebras and characterize those algebras with quadratic dimension 2. This will enable us to recover the classification of real oscillator algebras, a.k.a Lorentzian algebras, given by Medina et al. (Ann Sci École Norm Sup 18:553–561, 1985).

查看原文本刊更多论文

斜交映射与二次型李代数

向量空间的双扩展过程禀赋于非退化双线性形式，这使我们能够引入任意域 \(\mathbb {K}\) 上的广义 \(\mathbb {K}\) - 振荡器代数。我们将从基本的结构性质和斜联合内定形的典型形式出发，对二次零点有价代数的子类进行分类，并描述那些二次维数为 2 的代数的特征。这将使我们能够恢复梅迪纳等人给出的实振荡器代数（又称洛伦兹代数）的分类（Ann Sci École Norm Sup 18:553-561, 1985）。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.