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29 March 2024
 
  » arxiv » math.CO/0509133

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Noncommutative Symmetric Systems over Associative Algebras
Wenhua Zhao ;
Date 7 Sep 2005
Subject Combinatorics; Quantum Algebra MSC-class: Primary: 05E05, 14R10, 16W30; Secondary: 16W20, 06A11 | math.CO math.QA
AbstractThis paper is the first of a sequence papers (cite{GTS-II}--cite{GTS-V}) on the {it cNcs $( ext{noncommutative symmetric})$ systems} over differential operator algebras in commutative or noncommutative variables (cite{GTS-II}); the cNcs systems over the Grossman-Larson Hopf algebras (cite{GL}, cite{F}) of labeled rooted trees (cite{GTS-IV}); as well as their connections and applications to the inversion problem (cite{BCW}, cite{E}) and specializations of NCSF’s (cite{GTS-III}, cite{GTS-V}). In this paper, inspired by the seminal work cite{G-T} on NCSF’s (noncommutative symmetric functions), we first formulate the notion {it cNcs systems} over associative $Q$-algebras. We then prove some results for cNcs systems in general; the cNcs systems over bialgebras or Hopf algebras; and the universal cNcs system formed by the generating functions of certain NCSF’s in cite{G-T}. Finally, we review some of the main results that will be proved in the followed papers cite{GTS-II}, cite{GTS-IV} and cite{GTS-V} as some supporting examples for the general discussions given in this paper.
Source arXiv, math.CO/0509133
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