迹型到半单代数和群表示理论中的应用

Applying Trace Form to Semi-simple Algebras and Representation of Finite Groups

本文利用迹型证明了特征为0的域K上的半单代数存在本原中心幂等元完全系并且获得半单代数的直和分解,进而得到有限群常表示的一系列基本结果,这种方法比传统的方法(参见[1]和[2])简捷且明晰得多。

Using the trace form, we prove the existence of the complete set of primitive central idempotents of semi-simple algebra A on the field K of characteristic zero and exprese A as a direct sum of a finite number of irreducible submodules, further obtain a series of essential results of ordinary representation of finite groups. This method is shorter and clearer than the conventional methods ([1] or[2]).