73 research outputs found
The fundamental group of a Hopf linear category
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.Comment: Computations of the fundamental group of some Hopf algebras are
added. The relation with the fundamental group of the underlying associative
structure is now considered. We also analyse the situation when universal
covers and/or gradings exist. Dedicated to Eduardo N. Marcos for his 60th
birthday. 24 page
Invariants of a Free Linear Category and Representation Type
We consider an homogeneous action of a finite group on a free linear category
over a field in order to prove that the subcategory of invariants is still
free. Moreover we show that the representation type is preserved when
considering invariants.Comment: 19 page
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