Projective modules of 0-Schur algebras

We study the structure of the 0-Schur algebra S0(n,r)S0(n,r) following the geometric construction of S0(n,r)S0(n,r) by Jensen and Su [12]. The main results are the construction and classification of indecomposable projective modules. In addition, we construct bases of these modules and their homomorphism spaces. We also give a filtration of projective modules, which leads to a decomposition of S0(n,r)S0(n,r) into indecomposable left modules.