Mathematical Sciences: Hopf Algebras

本课题研究有限维Hopf代数的分类问题。最近，主要研究者证明了有限维Hopf代数是其任意Hopf子代数上的自由模。利用该自由定理及其相关技术，将小根Hopf代数、素维Hopf代数和低维Hopf代数进行分类。本课题的研究属于环理论的一般范畴。它特别关注Hopf代数。Hopf代数有许多应用，例如，在Kac-Moody代数，在群论和量子力学中。这个项目的成功结果将导致许多有用的应用。

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.