Abstract
A homomorphism of affine group schemes is a natural map G → H for which each G(R) → H(R) is a homomorphism. We have already seen the example det: GL n → G m . The Yoneda lemma shows as expected that such maps correspond to Hopf algebra homomorphisms. But since any map between groups preserving multiplication also preserves units and inverses, we need to check only that Δ is preserved. An algebra homomorphism between Hopf algebras which preserves Δ must automatically preserve S and ε.
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© 1979 Springer-Verlag New York Inc.
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Waterhouse, W.C. (1979). Affine Group Schemes: Examples. In: Introduction to Affine Group Schemes. Graduate Texts in Mathematics, vol 66. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-6217-6_2
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DOI: https://doi.org/10.1007/978-1-4612-6217-6_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6219-0
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