A Hopf module characterization of Hopf algebras

Radford, David E.

doi:10.1090/S0002-9939-1983-0691268-5

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A Hopf module characterization of Hopf algebras
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by David E. Radford PDF

Proc. Amer. Math. Soc. 88 (1983), 8-10 Request permission

Abstract:

A bialgebra over a field is a Hopf algebra if and only if all (nonzero) right Hopf modules are free, as modules, on a set of invariants.

References

David E. Radford, On bialgebras which are simple Hopf modules, Proc. Amer. Math. Soc. 80 (1980), no. 4, 563–568. MR 587928, DOI 10.1090/S0002-9939-1980-0587928-4
Moss E. Sweedler, Hopf algebras, Mathematics Lecture Note Series, W. A. Benjamin, Inc., New York, 1969. MR 0252485