On an analog of Lagrange’s theorem for commutative Hopf algebras
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- by David E. Radford
- Proc. Amer. Math. Soc. 79 (1980), 164-166
- DOI: https://doi.org/10.1090/S0002-9939-1980-0565330-9
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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.References
- Ulrich Oberst and Hans-Jürgen Schneider, Untergruppen formeller Gruppen von endlichem Index, J. Algebra 31 (1974), 10–44 (German). MR 360610, DOI 10.1016/0021-8693(74)90003-9
- David E. Radford, Freeness (projectivity) criteria for Hopf algebras over Hopf subalgebras, J. Pure Appl. Algebra 11 (1977/78), no. 1-3, 15–28. MR 476790, DOI 10.1016/0022-4049(77)90035-4
- David E. Radford, Pointed Hopf algebras are free over Hopf subalgebras, J. Algebra 45 (1977), no. 2, 266–273. MR 437582, DOI 10.1016/0021-8693(77)90326-X
- Moss E. Sweedler, Hopf algebras, Mathematics Lecture Note Series, W. A. Benjamin, Inc., New York, 1969. MR 0252485
- Mitsuhiro Takeuchi, A correspondence between Hopf ideals and sub-Hopf algebras, Manuscripta Math. 7 (1972), 251–270. MR 321963, DOI 10.1007/BF01579722 —, Commutative Hopf algebras are projective over Hopf subalgebras, preprint. —, On a semidirect product decomposition of affine groups over a field of characteristic 0, preprint.
Bibliographic Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 79 (1980), 164-166
- MSC: Primary 16A24; Secondary 14L17
- DOI: https://doi.org/10.1090/S0002-9939-1980-0565330-9
- MathSciNet review: 565330