Block of a Group Algebra

A block of a group algebra of a finite group over a field is a summand determined by a primitive central idempotent . The block idempotents are pairwise orthogonal and sum to 1, giving a direct product decomposition of the algebra. Every simple module belongs to exactly one block, characterized by acting as its identity. In modular representation theory, is finite and the field has prime characteristic . Blockwise counting uses Brauer characters, while Donovan's conjecture concerns Morita equivalence classes of blocks with bounded defect group order. A block in this sense is different from a block of a permutation group.