Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 17B50

Retrieve articles in all journals with MSC: 17B50


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0430009-X
PII: S 0002-9939(1976)0430009-X
Keywords: Hopf algebra, coradical, semidirect product
Article copyright: © Copyright 1976 American Mathematical Society