2022/07/09 by Mane Avetisyan, Avetisyan, Mane
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2207.04302
openalex publication_date 2022/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 S3 for each of the simple gauge groups, including the exceptional ones.