Constructing Quantum Groups and Hopf Algebras from Coverings Original Research Article

Given a group-graded free associative algebra, we show that in many cases the path algebra associated to the covering coming from the grading has a Hopf algebra structure. Our structure on the path algebra is that of a quantum group far most of these constructions. Adding more restrictions, we create some finite-dimensional quotients which inherit the structure of a Hoof algebra, usually a quantum group, from the path algebra.