Minimal Idempotents of Twisted Group Algebras of Cyclic 2-Groups

Idempotents in group algebras and minimal abelian codes

We compute the number of simple components of a semisimple finite abelian group algebra and determine all cases where this number is minimal; i.e. equal to the number of simple components of the rational group algebra of the same group. This result is used to compute idempotent generators of minimal abelian codes, extending results of Arora and Pruthi [S.K. Arora, M. Pruthi, Minimal cyclic code...

Idempotents in Group Algebras

In this survey we collect and present the classical and some recent methods to compute the primitive (central) idempotents in semisimple group algebras. MSC 2010. 20C05, 20C15, 16S34, 16U60.

Block Idempotents of Twisted Group Algebras1

In [4] Conlon has successfully generalized much of the theory of modular representations to the projective case. However his generalization [4, p. 166] of one of Brauer's main theorems on blocks [3, 10B], [5] is not entirely satisfactory. In Theorem 1 we present another generalization which is closer than Conlon's to the original Brauer theorem, and in Theorem 2 we indicate an application invol...

Central Idempotents in Group Algebras

Primitive Central Idempotents of Nilpotent Group Algebras

We exhibit the primitive central idempotents of a semisimple group algebra of a finite nilpotent group over an arbitrary field (without using group characters), examining the abelian case separately. Our result extends and improves the main result in [1].