On the Auslander-Reiten quiver of an infinitesimal group

Abstract

Let ${\cal G}$ be an infinitesimal group scheme, defined over an algebraically closed field of characteristic $p$. We employ rank varieties of ${\cal G}$-modules to study the stable Auslander-Reiten quiver of the distribution algebra of ${\cal G}$. As in case of finite groups, the tree classes of the AR-components are finite or infinite Dynkin diagrams, or Euclidean diagrams. We classify the components of finite and Euclidean type in case ${\cal G}$ is supersolvable or a Frobenius kernel of a smooth, reductive group.