Primitive Central Idempotents in Rational Group Algebras

Abstract

A complex irreducible character χ of a finite group G, with an affording representation ρ, is defined to have the property 𝒫 if, for all g ∈ G, either χ(g) = 0 or all the eigen-values of ρ(g) have the same order. An explicit expression for the primitive central idempotent of the rational group algebra ℚ[G] associated with a complex irreducible character having the property 𝒫 is derived. Several consequences are then obtained.

Key Words:

• Irreducible complex representation
• Primitive central idempotent
• Rational group algebra
• Wedderburn decomposition

2000 Mathematics Subject Classification:

• 16S34
• 20C05

Notes

Communicated by J. Zhang.