Decomposition of Finite-Dimensional Matrix Algebras over \mathbb{F}_{q}(y)

Abstract

Computing the structure of a finite-dimensional algebra is a classical mathematical problem in symbolic computation with many applications such as polynomial factorization, computational group theory and differential factorization. We will investigate the computational complexity and exhibit new algorithms for this problem over the field \mathbb{F}_{q}(y), where \mathbb{F}_{q} is the finite field with q elements. In this thesis we will present new efficient probabilistic algorithms for Wedderburn decomposition and the computation of the radical.