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.
2000 MATHEMATICS SUBJECT CLASSIFICATION:
Notes
1 It is noteworthy that Equation (27M) in Ref. [Citation6] should reduce to equation (12) in Ref. [Citation7] in this special case which, however, is actually not the case.
Siehler, J. A. (2003). Near-Group Categories, Ph.D. thesis, University Libraries, Virginia Polytechnic Institute and State University. Tambara, D., Yamagami, S. (1998). Tensor categories with fusion rules of self-duality for finite abelian groups. J. Algebra. 209(2):692–707. Additional information
Funding
Deutsche Forschungsgemeinschaft; SFB- TRR 195.