Mathematical Sciences: Hopf Algebras

本项目涉及的是 有限维Hopf代数最近，校长 研究者证明了有限维Hopf代数是一个 任意Hopf子代数上的自由模使用此 自由度定理及相关技巧， 研究者将对具有小余根Hopf代数进行分类， 素维数的Hopf代数与低维的Hopf代数 维度 本项目的研究范围为 戒指理论它特别关注的是霍普夫代数。 Hopf代数有许多应用，例如，在Kac-Moody 代数，群论和量子力学。一 该项目的成功结果将导致许多有益的 应用.

This project is concerned with the classification of finite dimensional Hopf algebras. Recently, the principal investigator proved that a finite dimensional Hopf algebra is a free module over its arbitrary Hopf subalgebras. Using this freeness theorem and the relevant techniques, the principal investigator will classify Hopf algebras with small coradical, Hopf algebras of prime dimension and Hopf algebras of low dimension. The research in this project is in the general area of ring theory. It is specifically concerned with Hopf algebras. Hopf algebras have many applications, for example, in Kac-Moody algebras, in group theory and in quantum mechanics. A successful outcome for this project would lead to many useful applications.