Homomorphisms, representations and amenability of group and Fourier algebras on locally compact groups

局部紧群上的群和傅里叶代数的同态、表示和适用性

• 批准号: 298444-2009
• 负责人: Stokke, Ross
• 金额: $ 0.66万
• 依托单位: University of Winnipeg
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2009
• 资助国家: 加拿大
• 起止时间: 2009-01-01 至 2010-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=427590
• 关键词: Homomorphisms; representations; amenability; group; Fourier

Locally compact groups are abstract mathematical objects which may be associated with the symmetries of a geometric figure, or the rigid motion of objects in nature. They have many applications, both to the mathematical and physical sciences. With any locally compact group, one can associate several useful collections of mappings into the set of real, or complex, numbers. An operator may be interpreted as a finite or infinite array of numbers, and there are also many relevant collections of operators associated to these locally compact groups. A Banach algebra is a collection of elements such that each individual element has a length, and such that any two elements can be added or multiplied. The aforementioned collections of functions and collections of operators are examples of Banach algebras, and this proposal is concerned with the study of various properties of these Banach algebras in relation to properties of their underlying locally compact groups.

局部紧群是抽象的数学对象，可能与几何图形的对称性或自然界中物体的刚性运动相关。它们在数学和物理科学方面都有很多应用。对于任何局部紧凑群，我们可以将几个有用的映射集合关联到一组实数或复数。运算符可以解释为有限或无限的数字数组，并且还有许多与这些局部紧凑组相关联的相关运算符集合。 巴纳赫代数是元素的集合，其中每个单独的元素都有长度，并且任意两个元素可以相加或相乘。上述函数集合和算子集合是 Banach 代数的示例，该提案涉及研究这些 Banach 代数与其基础局部紧群的属性相关的各种属性。