Mathematical Sciences: Classification and Characterization of Braided Tensor Categories

这个项目涉及到分类半简单的，辫子张量范畴，这些范畴是由一个单一的对象X产生的，X的张量平方与它自己的规定的分解。首席调查员还将研究编织类别的严密性问题及其在平衡阶段方面的特征。类别是对象的集合，以及地图的集合和地图的合成规则。一个例子是使用通常的函数组合的实线的子集上的函数集。类别最初的定义是为了填补数学中的一个基础角色。然而，目前范畴理论的研究主要集中在有结构的范畴上。这一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.