Computational Algebra Seminar: Brooksbank -- Algorithms for matrix algebras and their modules

Speaker: Peter Brooksbank (Bucknell University)
Title: Algorithms for matrix algebras and their modules
Time & Place: 3:05-4pm, Thursday 21 June, Eastern Ave Bldg, Rm 311

Abstract:
I will discuss new techniques for computing with matrix algebras
and their modules over arbitrary fields. The key is a deterministic algorithm
to construct a non-nilpotent element in any weakly-closed subset of a
non-nilpotent matrix algebra. There are immediate applications of this
construction to the problem of testing for isomorphism between two modules,
and to obtaining certain decompositions of a module. The methods are quite
elementary, requiring almost no structural knowledge of the algebra. Thus
the hope is that the resulting algorithms are practicable for a broad
range of fields, and I am particularly keen to discuss their practical
potential during my visit to Sydney. (This is joint work with Gene Luks at
the University of Oregon.)