On matched pairs defining Hopf algebras in a certain class

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.

Keywords:

• Hopf algebras
• matched pairs
• near-group categories

2000 MATHEMATICS SUBJECT CLASSIFICATION:

• 16W30

Notes

1 It is noteworthy that Equation (27M) in Ref. [6] should reduce to equation (12) in Ref. [7] in this special case which, however, is actually not the case.

Additional information

Funding

Deutsche Forschungsgemeinschaft; SFB- TRR 195.