Let K be an arbitrary field with no characteristic that divides the order of the dihedral group D2m of order 2m, where m is odd, and KD2m be the D2m group algebra over the field K. This paper investigates the structure of the semisimple dihedral group algebra KD2m. For this goal, we find a full system of minimum central orthogonal idempotents of the group algebra. We use it to define the basic components of KD2m and its Wedderburn decomposition. The results are as broad as feasible, requiring no limited field.
Plovdiv University ‘P. Hilendarski, 24 Tzar Asen Str., Plovdiv, Bulgaria.
Plovdiv University ‘P. Hilendarski’, 24 Tzar Asen Str., Plovdiv, Bulgaria.
Please see the link here: https://stm.bookpi.org/NRAMCS-V4/article/view/7038