Wedderburn Decomposition and Structure of a Semi-Simple Dihedral Group Algebra

Let be an arbitrary field, whose characteristic does not divide the order of the dihedral group of order , where is odd, and be the group algebra of over the field . The structure of the semisimple dihedral group algebra is examined in this work. We find a complete system of minimal central orthogonal idempotents of the group algebra for this purpose. We define the simple components of and its Wedderburn decomposition through it. The results are as general as possible, i.e. they do not require a finite field.