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Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1971 Nov;68(11):2631–2633. doi: 10.1073/pnas.68.11.2631

The Order of the Antipode of Finite-dimensional Hopf Algebra

Earl J Taft 1,2
PMCID: PMC389488  PMID: 16591950

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 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.

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