Some projective modules determined by sporadic geometries

A. J. E. Ryba, Stephen D. Smith and Satoshi Yoshiara

J. Algebra

Abstract

We determine which known sporadic geometries have projective Lefschetz modules.
An elementary lemma on local collapsibility greatly simplifies the task of
verifying projectivity. The modules are analyzed when possible in terms of
projective covers of individual irreducibles.