Non-Commutative Representations of Families of k^2 Commutative Polynomials in 2k^2 Commuting Variables
Rings and Algebras
2012-12-06 v1
Abstract
Given a collection P of k^2 commutative polynomials in 2k^2 commutative variables, the objective is to find a condensed representation of these polynomials in terms of a single non-commutative polynomial p(X,Y) in two k x k matrix variables X and Y. Algorithms that will generically determine whether the given family P has a non-commutative representation and that will produce such a representation are developed. These algorithms will determine a non-commutative representation for families P that admit a a non-commutative representation in an open, dense subset of the vector space of non-commutative polynomials in two variables.
Keywords
Cite
@article{arxiv.1212.0891,
title = {Non-Commutative Representations of Families of k^2 Commutative Polynomials in 2k^2 Commuting Variables},
author = {Harry Dym and J. W. Helton and Caleb Meier},
journal= {arXiv preprint arXiv:1212.0891},
year = {2012}
}