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 qn+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.
展开▼
机译：提供了一个域上有限维Hopf代数的示例，其对映体的映射具有≥4的任意偶数阶。 Hopf代数的维数是q n + 1 ，其中对映体的阶为2q，q≥2，n为任意正整数。代数不是半简单的，它们或它们的对偶代数都不是单模的。
展开▼
