2014 | OriginalPaper | Chapter
2. Modular Representations of Finite Groups
Author : Alexander Zimmermann
Published in: Representation Theory
Publisher: Springer International Publishing
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Abstract
We are now ready to apply the results from the previous chapter to group rings of finite groups. If the order of the group is invertible in the base field, Maschke’s Theorem 1.2.8 tells us that the group ring is semisimple, and semisimple rings are of less interest from the homological algebra point of view. Therefore, were are mostly interested in representations of finite groups \(G\) over fields \(k\) such that the characteristic of \(k\) divides the order of \(G\). In this chapter we will develop the classical part of the theory of these representations.