Projective modules of $0$-Schur algebras

Abstract

We study the structure of the $0$-Schur algebra $S_0(n,r)$ following the geometric construction of $S_0(n,r)$ by Jensen and Su \cite{JS}. 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 $S_0(n,r)$ into indecomposable left modules.

arXiv commentThe paper has been reorganised. Some results were removed and will appear elsewhere