ABSTRACT
At present, there is a great deal of work concerned with the actions of Hopf algebras on associative rings [7]. Much of this work has centered on the cases where the Hopf algebra is a group algebra KG [6], the dual of a group algebra (KG)* [2], or the enveloping algebra U(L) or restricted enveloping algebra u(L) of a Lie algebra [1], [5]. KG, U(L), and u(L) are cocommutative Hopf algebras, whereas (KG)* is a commutative Hopf algebra. However, recent work on quantum groups has fueled the interest in Hopf algebras which are neither commutative nor cocommutative. A difficulty in studying the actions of Hopf algebras which are neither commutative nor cocommutative has been a lack of concrete examples.
