Quantum complete rings and blocks with one simple module

Abstract

We generalize a construction of Benson and Green to realize a large class of quantum complete intersections as basic algebras of non-principal blocks of certain finite groups. The realization arises from an isomorphism of a quantum complete ring to a skew group ring. We also show that blocks of finite groups with normal abelian defect groups, abelian inertial quotients and, up to isomorphism, only one simple module have basic algebras amongst this class of quantum complete intersections. We also study the Ext rings and finite p′-coverings of these quantum complete intersections.