Primitive Central Idempotents in the Rational Group Algebras of Some Non-monomial Groups

Abstract

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It is well-known that every group algebra of a finite group over the field of rational numbers is isomorphic to a direct sum of finitely many matrix rings over division rings. This is the so-called Wedderburn-Artin decomposition. It follows that there are finitely primitive central idempotents in the rational group algebra. However, it is not easy to write down an explicit form for each primitive central idempotent when an arbitrary group is given. It is known that primitive central idempotents have a nice description for finite monomial groups and nilpotent groups. Such description is investigated by E. Jespers, A. Olivieri and Á. del Río. In this thesis, we focus on some non-monomial groups and give an explicit form for primitive central idempotents.