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

algebra;decomposition;radical;Wedderburn decomposition;Computer Science

Huang, Ruitong

University of Waterloo

关键词: algebra;    decomposition;    radical;    Wedderburn decomposition;    Computer Science;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/5360/1/4uw-ethesis.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

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 willpresent new efficient probabilistic algorithms for Wedderburn decomposition and the computation of the radical.