论文标题
沃格尔的普遍性及其应用
Vogel's Universality and its Applications
论文作者
论文摘要
本论文代表了与简单谎言代数相关的两个主要方向发展。第一个专门用于简单谎言代数的表示理论。具体而言，我们介绍了最新结果，其中包括Vogel通用描述中的新通用公式，以及发现这些公式的其他属性。在论文的第二部分中，我们证明了沃格尔描述在物理理论的研究中的应用。也就是说，我们明确地为每个简单量规组（包括杰出的量规组）上的$ s^3 $上的{\ IT完善} Chern-simons理论。
The present thesis represents developments in two main directions related to the simple Lie algebras. The first one is devoted to the representation theory of the simple Lie algebras. Specifically, we present recent results, which include new universal formulae in Vogel's universal description, as well as the discovery of additional properties of those formulae. In the second part of the thesis, we demonstrate applications of Vogel's description to the study of a physical theory. Namely, we explicitly formulate the { \it refined} Chern-Simons theories on $S^3$ for each of the simple gauge groups, including the exceptional ones.
