KTH/SU Mathematics Colloquium

08-06-18

Jon F. Carlson, UGA

Presentations for matrix algebras

In this lecture I will describe algorithms for obtaining presentations of matrix algebras. The results are joint work with Graham Matthews. The idea is to be able to construct examples in representation theory and homological algebra using computers. The programs not only compute generators and relations for a matrix algebra, they also construct a condensed version that is Morita equivalent to the origin alalgebra. Other calculations such as the dimension of the algebra, the Cartan matrix and the endomorphism ring are made easy in the process. A demonstration of the programs might be given. The programs run on the MAGMA system.