Computational Methods for Matrix Groups and Group Representations

矩阵群和群表示的计算方法

• 批准号: DP0452427
• 负责人: Prof John Cannon
• 金额: $ 25.07万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2004
• 资助国家: 澳大利亚
• 起止时间: 2004-01-01 至 2006-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP0452427
• 关键词: Computational; Methods; Matrix; Groups; Group

The symmetry of a system is captured mathematically by the notion of a group. A set of matrices closed under multiplication and the taking of inverses is an important example of a group. For instance, the symmetries of many physical systems and other objects are captured by a group of matrices over the complex numbers. This project will develop the computational tools necessary for constructing and analyzing finite matrix groups over infinite fields such as the complex numbers. These methods will find immediate application to many areas of science and engineering and, in particular, to the theory of quantum computation.

系统的对称性在数学上可以用群的概念来描述。一组在乘法和求逆运算下封闭的矩阵是群的一个重要例子。例如，许多物理系统和其他对象的对称性是由复数上的一组矩阵捕获的。本项目将开发必要的计算工具，用于构建和分析无限域（如复数）上的有限矩阵群。这些方法将立即应用于科学和工程的许多领域，特别是量子计算理论。