Noncommutative symmetric functions and W-polynomials

Details Noncommutative symmetric functions and W-polynomials Noncommutative symmetric functions and W-polynomials

2006-06-24

arxiv.org/abs/math/0606614v1

Mathematics

Rings and Algebras

Scientific paper

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.

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