Representations of Algebras: Some Computational Aspects

Abstract

Let n ϵ Z≥1 and R be a finitely presented k-algebra over a computable field k. We describe algorithms for computably deciding representation-theoretic properties of R, following work by Letzter. Among these algorithms is an algorithm deciding whether an n-dimensional irreducible representation exists. We also provide a package, finitely-presented-algebra, which implements these algorithms into the computer algebra system SAGE.