Block for a group

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Definition

Definition with symbols

Let G be a group and k a field. A block of G over k is a block of this algebra. Here,a a block of an algebra means one of the members of a maximal decomposition of the algebra as a direct sum of algebras.

In the case when the characteristic of k does not divide the order of G, the blocks are simply the matrix rings corresponding to the irreducible representations of G.

The theory of blocks becomes interesting in the case when the characteristic of k divides the order of G.