Wedderburn decomposition of finite group algebras

Wedderburn decomposition of finite group algebras

We show a method to effectively compute the Wedderburn decomposition and the primitive central idempotents of a semisimple finite group algebra of an abelian-by-supersolvable group G from certain pairs of subgroups of G. In this paper F = Fq denotes a finite field with q elements and G is a finite group of order n such that FG is semisimple, or equivalently (q, n) = 1. The group algebra FG is a...

Computing the Wedderburn decomposition of group algebras by the Brauer-Witt theorem

We present an alternative constructive proof of the Brauer–Witt theorem using the so-called strongly monomial characters that gives rise to an algorithm for computing the Wedderburn decomposition of semisimple group algebras of finite groups.

Algebras with Locally Finite Decomposition

We introduce the notion of locally finite decomposition rank, a structural property shared by many stably finite nuclear C∗-algebras. The concept is particularly relevant for Elliott’s program to classify nuclear C∗algebras by K-theory data. We study some of its properties and show that a simple unital C∗-algebra, which has locally finite decomposition rank, real rank zero and which absorbs the...

An algorithm to compute the Wedderburn decomposition of semisimple group algebras implemented in the GAP package wedderga

We present an algorithm to compute the Wedderburn decomposition of semisimple group algebras based on a computational approach of the Brauer-Witt theorem. The algorithm was implemented in the GAP package wedderga.

The Wedderburn Decomposition for Quotient Algebras Arising from Sets of Non-synthesis