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

Molnar, Richard K.

doi:10.1090/S0002-9939-1976-0430009-X

A semidirect product decomposition for certain Hopf algebras over an algebraically closed field
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by Richard K. Molnar

Proc. Amer. Math. Soc. 59 (1976), 29-32

DOI: https://doi.org/10.1090/S0002-9939-1976-0430009-X

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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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