Pointed Hopf actions on fields, II

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• 作者：Pavel Etingof^a ; ^{etingof@math.mit.edu" class="auth_mail" title="E-mail the corresponding author} ; Chelsea Walton^b ; ^{notlaw@temple.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：13B05 ; 16T05 ; 81R50
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：15 August 2016
• 年：2016
• 卷：460
• 期：Complete
• 页码：253-283
• 全文大小：604 K

文摘

This is a continuation of the authors' study of finite-dimensional pointed Hopf algebras H which act inner faithfully on commutative domains. As mentioned in Part I of this work, the study boils down to the case where H acts inner faithfully on a field. These Hopf algebras are referred to as Galois-theoretical.

In this work, we provide classification results for finite-dimensional pointed Galois-theoretical Hopf algebras H of finite Cartan type. Namely, we determine when such H   of type ${\mathrm{A}}_1^{\times r}$ and some H of rank two possess the Galois-theoretical property. Moreover, we provide necessary and sufficient conditions for Reshetikhin twists of small quantum groups to be Galois-theoretical.