The fundamental group of a Hopf linear category

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• 作者：Claude Cibils^a ; ^{Claude.Cibils@umontpellier.fr" class="auth_mail" title="E-mail the corresponding author} ; Andrea Solotar^b ; ^{asolotar@dm.uba.ar" class="auth_mail" title="E-mail the corresponding author}
• 关键词：16T05 ; 16W50 ; 14H30 ; 18D10 ; 18D20
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：15 September 2016
• 年：2016
• 卷：462
• 期：Complete
• 页码：137-162
• 全文大小：483 K

文摘

We define the fundamental group of a Hopf algebra over a field. For this purpose we first consider gradings of Hopf algebras and Galois coverings. The latter are given by linear categories with new additional structure which we call Hopf linear categories over a finite group. We compare this invariant to the fundamental group of the underlying linear category, and we compute those groups for families of examples.