A short note on Wedderburn decomposition of a group algebra

被引：1
|
作者：
Mittal, Gaurav [1 ,2 ]
Sharma, R. K. [3 ]
机构：
[1] Def Res & Dev Org, Near Metcalfe House, New Delhi 110054, India
[2] Indian Inst Technol Roorkee, Dept Math, Roorkee 247667, India
[3] Indian Inst Technol Delhi, Dept Math, New Delhi 110016, India
来源：
EXAMPLES AND COUNTEREXAMPLES | 2023年 / 3卷
关键词：
Wedderburn decomposition; Unit group; Representation theory; SEMISIMPLE GROUP-ALGEBRA;
D O I：
10.1016/j.exco.2023.100105
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we extend the result of Mittal and Sharma (Bull. Korean Math. Soc. 2022) on Wedderburn decomposition (WD) of a finite semisimple group algebra. It is known that, under certain conditions, WD of a finite semisimple group algebra FqG can be computed from WD of its subalgebra Fq(G/H), where H is a normal subgroup of G of prime order and q=pk for some prime p and positive integer k. We extend this result to any normal subgroup H of G of order n.
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