2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61757We prove that, over an algebraically closed field of characteristic zero, a semisimple Hopf algebra that has a nontrivial self-dual simple module must have even dimension. This generalizes a classical result of W. Burnside. As an application, we show under the same assumptions that a semisimple Hopf algebra that has a simple module of even dimension must itself have even dimension.9 pages. Important new result included. See also http://www.mathematik.uni-muenchen.de/~sommerhRings and AlgebrasQuantum AlgebraRepresentation Theory16W30text