Mathematical Sciences: Hopf Algebras

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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.