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.
No takes yet. Share an insight, caveat, or question.
Earl J. Taft (1971) studied this question.