Effective computation of SO(3) and O(3) linear representation symmetry classes

IF 1 Q4 MECHANICS

Mathematics and Mechanics of Complex Systems Pub Date : 2017-09-06 DOI:10.2140/memocs.2019.7.203

M. Olive

引用次数: 15

Abstract

We propose a general algorithm to compute all the symmetry classes of any $\mathrm{SO}(3)$ or $\mathrm{O}(3)$ linear representation. This method relies on the introduction of a binary operator between sets of conjugacy classes of closed subgroups, called the clips. We compute explicit tables for this operation which allows to solve definitively the problem.

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SO(3)和O(3)线性表示对称类的有效计算

我们提出了一种通用算法来计算任意$\mathrm{SO}(3)$或$\mathrm{O}(3)$线性表示的所有对称类。这种方法依赖于在闭子群的共轭类集合之间引入一个二元算子，称为clip。我们为这个操作计算了明确的表，从而可以明确地解决问题。

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

Mathematics and Mechanics of Complex Systems MECHANICS-

CiteScore

3.00

自引率

5.30%

发文量

期刊介绍： MEMOCS is a publication of the International Research Center for the Mathematics and Mechanics of Complex Systems. It publishes articles from diverse scientific fields with a specific emphasis on mechanics. Articles must rely on the application or development of rigorous mathematical methods. The journal intends to foster a multidisciplinary approach to knowledge firmly based on mathematical foundations. It will serve as a forum where scientists from different disciplines meet to share a common, rational vision of science and technology. It intends to support and divulge research whose primary goal is to develop mathematical methods and tools for the study of complexity. The journal will also foster and publish original research in related areas of mathematics of proven applicability, such as variational methods, numerical methods, and optimization techniques. Besides their intrinsic interest, such treatments can become heuristic and epistemological tools for further investigations, and provide methods for deriving predictions from postulated theories. Papers focusing on and clarifying aspects of the history of mathematics and science are also welcome. All methodologies and points of view, if rigorously applied, will be considered.