Structure of a semisimple dihedral group algebra

Abstract

Let K be an arbitrary field, whose characteristic does not divide the order of the dihedral group D2m of order 2m, where m is odd. In this paper we examine the structure of the semisimple dihedral group algebra KD2m . For this purpose, we find a complete system of minimal central orthogonal idempotents of the group algebra. Through it we define the minimal components of KD2m and its Wedderburn decomposition. The results we get are as general as possible, i.e. without requiring the field to be finite.