Structure of finite dihedral group algebra

In this article, we show explicitly all central irreducible idempotents and their Wedderburn decomposition of the dihedral group algebra FqD2nFqD2n, in the case when every divisor of n   divides q−1q−1.This characterization depends to the relation of the irreducible idempotents of the cyclic group algebra FqCnFqCn and the central irreducible idempotents of the group algebras FqD2nFqD2n.