Abstract
Throughout this note K will denote a field of characteristic p > 0. Let I be the set {1,2, … , m}, and a finite additive group of functions on I with values in K. We assume that is total in the sense that, for any λ1, … , λm in K Σi=imλiσ(i) = 0 for all a in G implies all σi = 0. It is clear that is an elementary p-group. Let pn be the order of . A generalized Witt algebra is defined as an algebra over K with basis elements {e(σ, i)∣ σ ∈ , i ∈ I} and the multiplication table is a simple Lie algebra except when p = 2, m = 1.
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