An explicit classification of dual pairs in exceptional Lie algebras

IF 0.8 4区 数学 Q2 MATHEMATICS
Marisa Gaetz
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引用次数: 0

Abstract

The primary goal of this paper is to explicitly write down all semisimple dual pairs in the complex exceptional Lie algebras. (A dual pair in a reductive Lie algebra g is a pair of subalgebras such that each member equals the other’s centralizer in g.) In a 1994 paper, H. Rubenthaler outlined a process for generating a complete list of candidate dual pairs in each of the complex exceptional Lie algebras. However, the process of checking whether each of these candidate dual pairs is in fact a dual pair is not easy: it requires the development of several distinct methods and the adaptation of results from multiple sources, some of which are not readily available online. In this paper, we carry out this process and explain the relevant concepts as we go. We also give plenty of examples with the hopes of making Rubenthaler’s 1994 result not only more complete but more usable and understandable.
例外李代数中对偶对的显式分类
本文的主要目的是明确地写出复例外李代数中所有的半简单对偶对。(约化李代数g中的对偶对是一对子代数,其中每一个元素都等于另一个在g中的扶正子。)在1994年的一篇论文中,H. Rubenthaler概述了在每个复例外李代数中生成候选对偶对的完整列表的过程。然而,检查这些候选双对中的每一个是否实际上是一对双对的过程并不容易:它需要开发几种不同的方法并适应来自多个来源的结果,其中一些来源并不容易在网上获得。在本文中,我们进行了这个过程,并解释了相关的概念。我们还提供了大量的例子,希望使Rubenthaler 1994年的结果不仅更完整,而且更易于使用和理解。
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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
41
审稿时长
40 days
期刊介绍: Our aim is to publish papers of interest to a wide mathematical audience. Our main interest is in expository articles that make high-level research results more widely accessible. In general, material submitted should be at least at the graduate level.Main articles must be written in such a way that a graduate-level research student interested in the topic of the paper can read them profitably. When the topic is quite specialized, or the main focus is a narrow research result, the paper is probably not appropriate for this journal. Most original research articles are not suitable for this journal, unless they have particularly broad appeal.Mathematical notes can be more focused than main articles. These should not simply be short research articles, but should address a mathematical question with reasonably broad appeal. Elementary solutions of elementary problems are typically not appropriate. Neither are overly technical papers, which should best be submitted to a specialized research journal.Clarity of exposition, accuracy of details and the relevance and interest of the subject matter will be the decisive factors in our acceptance of an article for publication. Submitted papers are subject to a quick overview before entering into a more detailed review process. All published papers have been refereed.
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