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Tag Archives: modular representation theory
Modular Representation Theory (IV)
Continuing our discussion of modular representation theory, we will now discuss block theory. Previously, we saw that in any ring R, there is at most one way to write where is a set of orthogonal and centrally primitive idempotents. If such an … Continue reading
Modular Representation Theory (III)
Let’s work out some explicit examples of modular characters. First, we have a summary of the main results. Let be the modular characters of the simple k[G]modules; they form a basis of Let be those of the projective indecomposable k[G]modules; they form a basis … Continue reading
Modular Representation Theory (II)
We continue our discussion of modular representations; recall that all modules are finitelygenerated even if we do not explicitly say so. First, we introduce a new notation: for each projective finitelygenerated k[G]module P, we have a unique projective finitelygenerated R[G]module denoted for which … Continue reading
Modular Representation Theory (I)
Let K be a field and G a finite group. We know that when char(K) does not divide G, the group algebra K[G] is semisimple. Conversely we have: Proposition. If char(K) divides G, then K[G] is not semisimple. Proof Let , a twosided … Continue reading