Block for a group

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 $G$.