# Lie algebras of algebraic groups

Where can i find material about the definition of the exponential morphism from the Lie algebra of an algebraic affine group to the group?

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Have you tried Waterhouse's "Introduction to Affine Algebraic Groups" especially part 3? –  stankewicz May 4 '11 at 19:21
What's up doc? Don't you know that $e^x$ is not usually a polynomial?? Thus, you have exponential maps only for nilpotent algebraic groups. In general, ther are some horrible formal guys living in some sort of hyperalgebra! Maybe, you start by explaining what you really want from your exponentials... –  Bugs Bunny May 4 '11 at 20:42
Have you looked at the famous Steinberg notes on Chevalley groups? –  isildur May 5 '11 at 0:23
As these comments illustrate, you need to provide more context for the question including restrictions on the ground field. –  Jim Humphreys May 5 '11 at 12:44

Over fields of characteristic $p>0$ it's also possible to make some use of the exponential power series, but only when applied to "nilpotent" elements of a restricted Lie algebra (also called Lie $p$-algebra) satisfying $x^{[p]}=0$. Such Lie algebras arise from linear algebraic groups, since the $p$-th power of a derivation is again a derivation. This technique continues to be useful in specialized questions involving nilpotent elements, although Chevalley's 1950s approach in characteristic 0 has been bypassed in favor of more powerful geometric techniques.