Truncated induced modules over transitive Lie algebras of characteristic $p$

By constructing truncated coinduced modules a theorem is proved on the minimal imbedding of a transitive Lie algebra over a perfect field into the Lie algebra $W(\mathscr F)$. A formula for cohomology with coefficients in a truncated induced module is obtained. A description is given of filtered Lie algebras over a perfect field associated with graded Lie algebras of Cartan type and their derivations. Cartan prolongations of truncated induced modules are investigated.
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