Abstract
Using results on algebras that are graded by p-groups, we study representations of infinitesimal groups \( \mathcal{G} \) that possess a normal subgroup \( \mathcal{N}\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \triangleleft } \mathcal{G} \) with a diagonalizable factor group \( \mathcal{G} \mathord{\left/ {\vphantom {\mathcal{G} \mathcal{N}}} \right. \kern-\nulldelimiterspace} \mathcal{N} \). When combined with rank varieties, Auslander-Reiten theory and Premet's work on SL(2)1-modules, these techniques lead to the determination of the indecomposable modules of the infinitesimal groups of domestic representation type.
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