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

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