Structure of Finite dihedral group algebra

Abstract: In this article, we show the relation between the irreducible idempotents of the cyclic group algebra $\mathbb F_qC_n$ and the central irreducible idempotents of the group algebras $\mathbb F_qD_{2n}$, where $\mathbb F_q$ is a finite field with $q$ elements and $D_{2n}$ is the dihedral group of order $2n$, where ${\rm gcd}(q,n)=1$.