Fast Matrix Multiplication and the Wedderburn-Artin Theorem

Researchers Cohn and Umans proposed a framework for fast matrix multiplication algorithms. Their approach is reliant on an application of the Wedderburn-Artin Theorem: a landmark classification result in modern algebra. We show experimental success for algebras whose components all have dimension 1. We advance the Cohn and Umans framework by developing new, extendable tools to couple with their design

Describing units of integral group rings up to commensurability

We restrict the types of 2×2-matrix rings which can occur as simple components in the Wedderburn decomposition of the rational group algebra of a finite group. This results in a description up to commensurability of the group of units of the integral group ring ZG for all finite groups G that do not have a non-commutative Frobenius complement as a quotient

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

AbstractWe 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