Limits of coalgebras, bialgebras and Hopf algebras Vrije Universiteit Brussel
of two morphisms of coalgebras (resp. bialgebras, Hopf algebras) are also described explicitly. As a consequence the categories of ...
We completely describe by generators and relations and classify all Hopf algebras which factorize through the Taft algebra T m 2 (q) and the group Hopf algebra K[C n]: they are nm 2-dimensional quantum groups T ω nm2(q) associated to an n-th root of unity ω. Furthermore, using Dirichlet’s prime number theorem we are able to count the number of isomorphism types of such Hopf algebras. More precisely, if d = gcd(m,v(n)) and {Formula presented} ...
We introduce the notion of support equivalence for (co)module algebras (over Hopf algebras), which generalizes in a natural way (weak) an equivalence of gradings. We show that for each equivalence class of (co)module algebra structures on a given algebra A, there exists a unique universal Hopf algebra H together with an H -(co)module structure on A such that any other equivalent (co)module algebra structure on A factors through the action of ...
We develop a theory which unifies the universal (co)acting bi/Hopf algebras as studied by Sweedler, Manin and Tambara with the recently introduced [A. L. Agore, A. S. Gordienko and J. Vercruysse, On equivalences of (co)module algebra structures over Hopf algebras, J. Noncommut. Geom., doi: 10.4171/JNCG/428.] bi/Hopf-algebras that are universal among all support equivalent (co)acting bi/Hopf algebras. Our approach uses vector spaces endowed ...