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A correspondence between Hopf ideals and sub-Hopf algebras

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Abstract

In this paper we show a bijective correspondence between normal Hopf ideals and sub-Hopf algebras of a commutative Hopf algebra over a field k. This gives a purely algebraic proof of the fundamental theorem [2, III, §3, no7] of the theory of affine k-groups.

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References

  1. Bourbaki, N.: Algèbre commutative, Paris: Hermann 1961.

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  2. Demazure, M. et Gabriel, P.: Groupes algébriques, tome I, Paris: Masson & Cie., Amsterdam: North-Holland 1970.

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  3. Sweedler, M. E.: Hopf algebras, New York: Benjamin 1969.

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Authors and Affiliations

  1. Department of Mathematics, Tokyo Metropolitan University, Fukazawa-cho, Setagaya, Tokyo, Japan

    Mitsuhiro Takeuchi

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  1. Mitsuhiro Takeuchi
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Takeuchi, M. A correspondence between Hopf ideals and sub-Hopf algebras. Manuscripta Math 7, 251–270 (1972). https://doi.org/10.1007/BF01579722

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  • DOI: https://doi.org/10.1007/BF01579722

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