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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On an analog of Lagrange's theorem for commutative Hopf algebras


Author: David E. Radford
Journal: Proc. Amer. Math. Soc. 79 (1980), 164-166
MSC: Primary 16A24; Secondary 14L17
MathSciNet review: 565330
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Abstract: We show that the Hopf algebra A over any field k representing the affine group scheme $ {\text{SL}}(2,)$ is not a free B-module for some sub-Hopf algebra B of A. In particular k can be algebraically closed, or of characteristic 0 in which case A is also cosemisimple.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0565330-9
PII: S 0002-9939(1980)0565330-9
Keywords: Hopf algebra, free module
Article copyright: © Copyright 1980 American Mathematical Society