On matched pairs defining Hopf algebras in a certain class

Abstract

Abstract In previous work by the author, a class of finite-dimensional semisimple Hopf algebras was considered with respect to the question under what condition all but one isomorphism class of simple modules are one-dimensional. The group theoretical answer given there asks for a classification of certain matched pairs used for the construction of these Hopf algebras. This classification is the content of this paper.