Constructing quantum groups and Hopf algebras from coverings
Let \(G\) be a finite group, \(W:\{1,\dots, n\} \to G\) a weight function, \(\Gamma\) the directed graph associated to \(W\) and \(K\Gamma\) the corresponding path algebra over a field \(K\). If the image of \(W\) is contained in the center of \(G\), then any choice of multiplicative characters \(f_i:G \to K^\times\), \(1 \leq i \leq n\), determines a Hopf algebra structure on the path algebra \(K \Gamma\). If \(f_i(W_j)=f_j(W_i)^{-1}\) for \(i \neq j\) then \(K \Gamma\) has a finite dimensional Hopf algebra quotient. This construction generalizes that given by \textit{C. Cibils} [Commun. Math. Phys. 157, No. 3, 459-477 (1993; Zbl 0806.16039)].
finite dimensional Hopf algebra quotients
scientific article; zbMATH DE number 802367