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 F q D 2 n , in the case when every divisor of n divides q - 1 .This characterization depends to the relation of the irreducible idempotents of the cyclic group algebra F q C n and the central irreducible idempotents of the group algebras F q D 2 n .