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

MathSciNet review:
0430009

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Abstract: Let be a finite dimensional Hopf algebra over an algebraically closed field. We show that if is commutative and the coradical is a sub Hopf algebra, then the canonical inclusion has a Hopf algebra retract; or equivalently, if is cocommutative and the Jacobson radical is a Hopf ideal, then the canonical projection has a Hopf algebra section.

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

Keywords:
Hopf algebra,
coradical,
semidirect product

Article copyright:
© Copyright 1976
American Mathematical Society