Block for a group
Definition with symbols
Let be a group and a field. A block of over 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 does not divide the order of , the blocks are simply the matrix rings corresponding to the irreducible representations of .
The theory of blocks becomes interesting in the case when the characteristic of divides the order of .