Algebraic Transformation Groups

代数变换群

• 批准号: 341744-2012
• 负责人: Kuttler, Jochen
• 金额: $ 1.09万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=549468
• 关键词: Algebraic; Transformation; Groups

In mathematics, the symmetries of an object or structure is captured by the group of symmetry transformations that preserve it. At an elementary level this starts with the rotations, translations, and combinations thereof, which preserve a wallpaper pattern. On a more advanced level this leads to the symmetry groups of crystals in chemistry, or of protein structures in biology, or for instance the requirements of special relativity that the laws of motion must be invariant under Lorentz transformations.

在数学中，一个物体或结构的对称性是通过一组保持它的对称变换来体现的。在基本的层面上，这是从旋转、平移和它们的组合开始的，这些都保留了墙纸的图案。在更高级的层面上，这导致了化学中晶体的对称群，或者生物学中蛋白质结构的对称群，或者例如狭义相对论的要求，即运动定律在洛伦兹变换下必须不变。