Projective Indecomposable

Some articles on projective indecomposable, projective:

Modular Representation Theory - Decomposition Matrix and Cartan Matrix
... The composition factors of the projective indecomposable modules may be calculated as follows Given the ordinary irreducible and irreducible Brauer ... simple modules as composition factors of the j-th projective indecomposable module ... Since a projective indecomposable module in a given block has all its composition factors in that same block, each block has its own Cartan matrix ...
Modular Representation Theory - Some Orthogonality Relations For Brauer Characters
... When a projective module is lifted, the associated character vanishes on all elements of order divisible by p, and (with consistent choice of roots of unity ... inner product of the Brauer character of a projective indecomposable with any other Brauer character can thus be defined this is 0 if the second Brauer character is that of the socle of a non-isomorphic ... character in the character of the lift of a projective indecomposable is equal to the number of occurrences of the Brauer character of the socle of the ...