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- Title
NON-COMMUTATIVE REPRESENTATIONS OF FAMILIES OF k<sup>2</sup> COMMUTATIVE POLYNOMIALS IN 2k<sup>2</sup> COMMUTING VARIABLES.
- Authors
DYM, HARRY; HELTON, J. WILLIAM; MEIER, CALEB
- Abstract
Given a collection of k2 commutative polynomials in 2k2 variables, the objective is to find a condensed representation for these polynomials in terms of a single non-commutative (nc) polynomial p(X, Y) in two k × k matrix variables X and Y. In this paper, we develop algorithms that will generically determine whether the given family has a nc representation and will produce such a representation if it exists. In particular, we determine an open, dense subset of the space of nc polynomials in two variables that satisfies the following property: if a family of polynomials admits a nc representation in this subset, then our algorithms will determine this representation.
- Subjects
NONCOMMUTATIVE algebras; REPRESENTATION theory; COMMUTATIVE algebra; POLYNOMIALS; MATHEMATICAL variables
- Publication
International Journal of Algebra & Computation, 2013, Vol 23, Issue 7, p1685
- ISSN
0218-1967
- Publication type
Article
- DOI
10.1142/S0218196713500422