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Proceedings of the American Mathematical Society

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

 

 

A correspondence theorem for modules over Hopf algebras


Author: Jeffrey Bergen
Journal: Proc. Amer. Math. Soc. 121 (1994), 343-345
MSC: Primary 16W30; Secondary 16S40
DOI: https://doi.org/10.1090/S0002-9939-1994-1211578-X
MathSciNet review: 1211578
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Abstract: Let H be a finite-dimensional Hopf algebra. We prove that if M is a faithful H-module and if $ {H_1} \ne {H_2}$ are sub-Hopf algebras of H, then $ {M^{{H_1}}} \ne {M^{{H_2}}}$, where $ {M^{{H_1}}}$ and $ {M^{{H_2}}}$ are the invariants in M under the respective actions of $ {H_1}$ and $ {H_2}$. We also show that if $ {H_1} \ne {H_2}$, then $ {H_1}$ and $ {H_2}$ have different left integrals. Both of these results rely heavily on the freeness theorem of Nichols-Zoeller.


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DOI: https://doi.org/10.1090/S0002-9939-1994-1211578-X
Article copyright: © Copyright 1994 American Mathematical Society