Abstract
The idea on which this part is based is an algebraic version ofdifferentiation which will serve in all characteristics as a replacement for the “differential” part of real Lie group theory. The crucial feature turns out to be the product rule. Specifically, let A be a k-algebra, M an A-module. A derivation D of A into M is an additive map D: A → M satisfying D(ab) = aD(b) + bD(a). We say D is a k-derivation if it is k-linear, or equivalently if D(k) = 0. Ultimately k here will be a field, but for the first three sections it can be any commutative ring.
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© 1979 Springer-Verlag New York Inc.
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Waterhouse, W.C. (1979). Differentials. 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_11
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DOI: https://doi.org/10.1007/978-1-4612-6217-6_11
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