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We describe the structure of projective indecomposable modules for thesubalgebra consisting of the elements of degree 0 in the hyperalgebra of the$r$-th Frobenius kernel for the algebraic group ${\rm SL}_2(k)$, using theprimitive idempotents which were constructed before by the author.

Projective modules for the subalgebra of degree 0 in a finite-dimensional hyperalgebra of type $A_1$