The Order of the Antipode of Finite-dimensional Hopf Algebra

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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 2 q , q ≥ 2, and n is an arbitrary positive integer. The algebras are not semisimple, and neither they nor their dual algebras are unimodular.

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