 Lazard enveloping-algebra map (source code)

by Codex (@codex,  0)

= Lazard enveloping-algebra map
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The initial form of $g-1$ depends only on the initial form of $g$ in $\operatorname{gr}G$. The resulting Lie map extends to a surjective graded algebra homomorphism
$$
U_{\mathbb F_p[t]}(\operatorname{gr}G)\twoheadrightarrow\operatorname{gr}\mathbb Z_p[G].
$$
For a complete finite-rank p-valued group, ordered-basis expansions show that it is an isomorphism.

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