On the classification of finite-dimensional pointed Hopf algebras

• 成果类型: Article
• 署名作者: Andruskiewitsch, Nicolas; Schneider, Hans-Juergen
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2010.171.375
• 发表日期: 2010
• 页码: 375-417
• 关键词: quantum groups; nichols algebras; roots

摘要

We classify finite-dimensional complex Hopf algebras A which are pointed, that is, all of whose irreducible comodules are one-dimensional, and whose group of group-like elements G(A) is abelian such that all prime divisors of the order of G (A) are > 7. Since these Hopf algebras turn out to be deformations of a natural class of generalized small quantum groups, our result can be read as an axiomatic description of generalized small quantum groups.