Tag Archives: modular representation theory

Modular Representation Theory (IV)

Posted on March 13, 2015 by

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 →

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Modular Representation Theory (III)

Posted on February 27, 2015 by

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 →

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Modular Representation Theory (II)

Posted on February 17, 2015 by

We continue our discussion of modular representations; recall that all modules are finitely-generated even if we do not explicitly say so. First, we introduce a new notation: for each projective finitely-generated k[G]-module P, we have a unique projective finitely-generated R[G]-module denoted for which … Continue reading →

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Modular Representation Theory (I)

Posted on February 10, 2015 by

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 two-sided … Continue reading →

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