A short note on Wedderburn decomposition of a group algebra

Abstract

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 FqGcan be computed from WD of its subalgebra Fq(G/H), where H is a normal subgroup of G of prime order and q=pkfor some prime p and positive integer k. We extend this result to any normal subgroup H of G of order n.

Keywords

• Wedderburn decomposition
• Unit group
• Representation theory