Primitive cohomology of Hopf algebras

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• 作者：D.-G. Wang^a ; ^{dgwang@mail.qfnu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; ^{dingguo95@126.com" class="auth_mail" title="E-mail the corresponding author} ; J.J. Zhang^b ; ^{zhang@math.washington.edu" class="auth_mail" title="E-mail the corresponding author} ; G. Zhuang^c ; ^{gzhuang@usc.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 16T05 ; 16E65 ; secondary ; 16S34 ; 16S40
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：15 October 2016
• 年：2016
• 卷：464
• 期：Complete
• 页码：36-96
• 全文大小：888 K

文摘

Primitive cohomology of a Hopf algebra is defined by using a modification of the cobar construction of the underlying coalgebra. Among many of its applications, two classifications are presented. Firstly we classify all non-locally PI, pointed Hopf algebra domains of Gelfand–Kirillov dimension two; and secondly we classify all pointed Hopf algebras of rank one. The first classification extends some results of Brown, Goodearl and others in an ongoing project to understand all Hopf algebras of low Gelfand–Kirillov dimension. The second generalizes results of Krop–Radford and Wang–You–Chen which classified Hopf algebras of rank one under extra hypothesis. Properties and algebraic structures of the primitive cohomology are discussed.