Hopf algebras and quantum groups

Hopf 代数和量子群

• 批准号: 9137-2010
• 负责人: Beattie, Margaret
• 金额: $ 1.09万
• 依托单位: Mount Allison University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2011
• 资助国家: 加拿大
• 起止时间: 2011-01-01 至 2012-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=474504
• 关键词: Hopf; algebras; quantum; groups

The study of symmetry is central to the mathematical and physical sciences and symmetry is expressed mathematically in the language of groups. More subtle forms of symmetry require more sophisticated mathematical notions. One of these is the notion of quantum symmetry, so that for example, rather than having a simple relation of the form ab equals ba, we have that ab is qba, in other words ab and ba are equal up to a factor of q. This notion occurs naturally in the physical world.

对对称性的研究是数学和物理科学的核心，对称性在数学上用群的语言表达。 更微妙的对称形式需要更复杂的数学概念。其中之一是量子对称性的概念，因此，例如，我们不是有一个简单的关系式ab等于ba，而是有ab是qba，换句话说，ab和ba在一个因子q之前是相等的。 这个概念在物理世界中自然发生。