Simultaneous direct sum decompositions of several multivariate polynomials
Rings and Algebras
2025-03-11 v2
Abstract
We consider the problem of simultaneous direct sum decomposition of a set of multivariate polynomials. To this end, we extend Harrison's center theory for a single homogeneous polynomial to this broader setting. It is shown that the center of a set of polynomials is a special Jordan algebra, and simultaneous direct sum decompositions of the given polynomials are in bijection with complete sets of orthogonal idempotents of their center algebra. Several examples are provided to illustrate the performance of this method.
Keywords
Cite
@article{arxiv.2503.01205,
title = {Simultaneous direct sum decompositions of several multivariate polynomials},
author = {Lishan Fang and Hua-Lin Huang and Lili Liao},
journal= {arXiv preprint arXiv:2503.01205},
year = {2025}
}