Mathematical Sciences: Classification and Characterization of Braided Tensor Categories

这个项目关注的是对由单个对象X生成的半简单的编织张量类别进行分类，这些类别具有X与自身的张量平方的规定分解。首席研究员还将研究编织类别的严格性问题及其在平衡阶段方面的表征。范畴是对象的集合，以及映射的集合和映射的组成规则。一个例子是使用通常的函数组合在实直线的子集上的函数集。分类最初是为了在数学中扮演基础角色而定义的。然而，目前的范畴理论研究主要关注具有结构的范畴。这个领域对数学的许多不同领域以及理论物理都有潜在的影响。

This project is concerned with classifying semisimple, braided tensor categories that are generated by a single object X with a prescribed decomposition of the tensor square of X with itself. The principal investigator will also work on the question of strictness of braided categories and their characterization in terms of balancing phases. A category is a collection of objects, together with a collection of maps and a rule of composition of maps. One example is the set of functions on subsets of the real line using the usual composition of functions. Categories were originally defined to fill a foundational role in mathematics. However, current research in category theory is concerned with categories with structure. This area has potential impact on a number of different areas of mathematics, as well as theoretical physics.