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A semidirect product decomposition for certain Hopf algebras over an algebraically closed field


Author: Richard K. Molnar
Journal: Proc. Amer. Math. Soc. 59 (1976), 29-32
MSC: Primary 17B50
DOI: https://doi.org/10.1090/S0002-9939-1976-0430009-X
MathSciNet review: 0430009
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Abstract: Let $ H$ be a finite dimensional Hopf algebra over an algebraically closed field. We show that if $ H$ is commutative and the coradical $ {H_0}$ is a sub Hopf algebra, then the canonical inclusion $ {H_0} \to H$ has a Hopf algebra retract; or equivalently, if $ H$ is cocommutative and the Jacobson radical $ J(H)$ is a Hopf ideal, then the canonical projection $ H \to H/J(H)$ has a Hopf algebra section.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0430009-X
Keywords: Hopf algebra, coradical, semidirect product
Article copyright: © Copyright 1976 American Mathematical Society

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