Some computations of Frobenius-Schur indicators of the regular representations of Hopf algebras

We study Frobenius-Schur indicators of the regular representations of finite-dimensional semisimple Hopf algebras, especially group-theoretical ones. Those of various Hopf algebras are computed explicitly. In view of our computational results, we formulate the theorem of Frobenius for semisimple Hopf algebras and give some partial results on this problem.