Noncommutative symmetric functions and W-polynomials
Rings and Algebras
2007-05-23 v1
Abstract
Let K,S,D be a division ring, an endomorphism and a S-derivation of K, respectively. In this setting we introduce generalized noncommutative symmetric functions and obtain Vieta formula and decompositions of differential operators. W-polynomials show up naturally, their connections with P-independency, Vandermonde and Wronskian matrices are briefly studied. The different linear factorizations of W-polynomials are analysed. Connections between the existence of LLCM of monic linear polynomials with coefficients in a ring and the left duo property are established at the end of the paper.
Cite
@article{arxiv.math/0606614,
title = {Noncommutative symmetric functions and W-polynomials},
author = {J. Delenclos and A. Leroy},
journal= {arXiv preprint arXiv:math/0606614},
year = {2007}
}