We describe a simple approach to factorize non-commutative (nc) polynomials, that is, elements in free associative algebras (over a commutative field), into atoms (irreducible elements) based on (a special form of) their minimal linear representations. To be more specific, a correspondence between factorizations of an element and upper right blocks of zeros in the system matrix (of its representation) is established. The problem is then reduced to solving a system of polynomial equations (with at most quadratic terms) with commuting unknowns to compute appropriate transformation matrices (if possible).
|Number of pages||22|
|Journal||arXiv.org e-Print archive|
|Publication status||Published - 6 Jun 2017|
- Primary 16K40, 16Z05, Secondary 16G99, 16S10