A complete classification up to isomorphism is given for simple W_ℓ-modules with p-characters of height ≤1, together with investigation of a family having height >1.
Strade, Simple Lie Algebras over Fields of Positive Characteristic I: Structure Theory
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Simple modules over truncated current Lie algebras of the Witt algebra
A complete classification up to isomorphism is given for simple W_ℓ-modules with p-characters of height ≤1, together with investigation of a family having height >1.