Categorical Hopf kernels and representations of semisimple Hopf algebras

It is shown that in the category of semisimple Hopf algebras the categorical Hopf kernels introduced by Andruskiewitsch and Devoto (1995) in [1] coincide with the kernels of representations introduced by the present author in 2009 [2]. New results concerning the normality of these kernels are also presented. It is proven that the Hopf algebra property to have all representation kernels as normal Hopi subalgebras is a self-dual property. (C) 2011 Elsevier Inc. All rights reserved.