The Order of the Antipode of Finite-dimensional Hopf Algebra
Abstract
Examples of finite-dimensional Hopf algebras over a field, whose antipodes have arbitrary even orders ≥4 as mappings, are furnished. The dimension of the Hopf algebra is q n+1, where the antipode has order 2q, q ≥ 2, and n is an arbitrary positive integer. The algebras are not semisimple, and neither they nor their dual algebras are unimodular.
