Structure of Hermitian groups and Group C*-algebras

点击翻译按钮获取中文摘要

Two important areas of mathematics are group theory and functional analysis. The first of these two topics, group theory, originally arose from the study of symmetries and has become one of the most fundamental structures in mathematics over the past couple of centuries. Group theory's applications are far reaching and the theory is frequently applied to physics, chemistry, materials science, and other areas. Functional analysis is a much more recent innovation, being initially developed in twentieth century. Some of the areas where functional analysis techniques are applied include image processing, economics, partial differential equations, and quantum physics. This project seeks to understand the structural properties of two functional analytic constructions arising from groups: the group algebra L1(G) and the full group C*-algebra C*(G), which are fundamental objects of study in the fields of Banach algebras, C*-algebras, and abstract harmonic analysis.