On idempotents in reduced enveloping algebras

Abstract

Explicit constructions are given for idempotents that generate all projective indecomposable modules for certain finite-dimensional quotients of the universal enveloping algebra of the Lie algebra s ℓ ( 2 ) s\ell (2) in odd prime characteristic. The program is put in a general context, although constructions are only carried through in the case of s ℓ ( 2 ) s\ell (2) .