论文标题
二面基团和广义四基群的基团代数的基本分解
Primitive decompositions of idempotents of the group algebras of dihedral groups and generalized quaternion groups
论文作者
论文摘要
在本文中，我们介绍了一种基于其矩阵表示和wedderburn分解的任何半圣经组代数的基本群的原始分解方法。特别是，我们使用此方法来计算二面体组代数$ \ mathbb {c} [d_ {2n}] $和概括的Quaternion组代数$ \ mathbb {c} [q__ {4m}] $。受这两个群体家族的角色表的正交关系的启发，我们获得了两组三角身份。此外，描述了$ \ mathbb {c} [d_ {8}] $和$ \ mathbb {c} [q_ {8}] $之间的一个组代数同构，在这些基础上，这两个完整的原始正交正交式构想的两种基团Algebras的构想我们都可以与每个其他基因进行对应。
In this paper, we introduce a method computing the primitive decomposition of idempotents of any semisimple finite group algebra based on its matrix representations and Wedderburn decomposition. Particularly, we use this method to calculate the examples of the dihedral group algebras $\mathbb{C}[D_{2n}]$ and generalized quaternion group algebras $\mathbb{C}[Q_{4m}]$. Inspired by the orthogonality relations of the character tables of these two families of groups, we obtain two sets of trigonometric identities. Furthermore, a group algebra isomorphism between $\mathbb{C}[D_{8}]$ and $\mathbb{C}[Q_{8}]$ is described, under which the two complete sets of primitive orthogonal idempotents of these two group algebras we find correspond to each other bijectively.
