The fundamental group of a Hopf linear category

Claude Cibils (1) , Andrea Solotar

1 IMAG - Institut Montpelliérain Alexander Grothendieck

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.

Mots clés: Fundamental group; Grading; Hopf category

Domaines: Catégories et ensembles [math.CT]; Algèbres quantiques [math.QA]; Anneaux et algèbres [math.RA]; Théorie des représentations [math.RT]

Claude Cibils, Andrea Solotar. The fundamental group of a Hopf linear category. Journal of Algebra, 2016, 462, pp.137-162. ⟨10.1016/j.jalgebra.2016.04.031⟩. ⟨hal-01382681⟩