Reducible $p$-representations of a simple three-dimensional Lie $p$-algebra
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (1982), pp. 45-49
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We study the category $\mathscr{P}$ of restricted finite-dimensional representations of the simple $3$-dimensional Lie algebra $L$. We show that $\mathscr{P}$ is equivalent to the sum of some categories of diagrams over finite dimensional vector spaces. We find the indecomposable objects in the latter categories. Thus we obtain a classification of indecomposable restricted representations of $L$ and an effective method of their construction.