通用根系的分类

IF 0.5 4区数学 Q3 MATHEMATICS

Archiv der Mathematik Pub Date : 2024-10-01 DOI:10.1007/s00013-024-02046-1

Michael Cuntz, Bernhard Mühlherr

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引用次数: 0

摘要

迪米特洛夫和费奥雷西提出了一个对象，他们称之为广义根系统。这是欧几里得空间中的有限矢量集合，满足角度和元素的和与差之间的某些兼容性。他们猜想，每一个广义根系都等价于一个与韦尔排列的限制相关联的根系。在本论文中，我们证明了这一猜想，并提供了广义根系统的完整分类，直至等价。

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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A classification of generalized root systems

Dimitrov and Fioresi introduced an object that they call a generalized root system. This is a finite set of vectors in a Euclidean space satisfying certain compatibilities between angles and sums and differences of elements. They conjecture that every generalized root system is equivalent to one associated to a restriction of a Weyl arrangement. In this note, we prove the conjecture and provide a complete classification of generalized root systems up to equivalence.

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来源期刊

Archiv der Mathematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

117

审稿时长

4-8 weeks

期刊介绍： Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.