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SRAC 2017: Advances in Algebra pp 95-109

# Computing with Matrix and Basic Algebras

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 277)

## Abstract

This is a survey of my lecture delivered at the Southern Regional Algebra Conference in March 2017. It is meant to demonstrate some of the methods and technology that can be used to investigate examples in the theory of representations of groups and algebras. The concentration is on using computational methods to determine the structure of a matrix algebra as in the theorems of Wedderburn and investigating homological properties of the algebra by way of its basic algebra. For every split finite-dimensional associative algebra, there is a basic algebra, one whose simple modules have dimension one, that has the same representation theory. In the computational setting, it is usually much more practical to first find the basic algebra when studying representation theory.

## Keywords

Matrix algebra Basic algebra Computational methods Idempotent decomposition

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## Copyright information

© Springer Nature Switzerland AG 2019

## Authors and Affiliations

1. 1.Department of MathematicsUniversity of GeorgiaAthensUSA