Mathematics – Combinatorics
Scientific paper
2005-09-07
J. Pure Appl. Algebra, 210 (2007), no. 2, 363--382
Mathematics
Combinatorics
A connection of NCS systems with combinatorial Hopf algebras of M. Aguiar, N. Bergeron and F. Sottile has been added in Remark
Scientific paper
This paper is the first of a sequence papers ([Z4]--[Z7]) on the {\it ${\mathcal N}$CS $(\text{noncommutative symmetric})$ systems} over differential operator algebras in commutative or noncommutative variables ([Z4]); the ${\mathcal N}$CS systems over the Grossman-Larson Hopf algebras ([GL],[F]) of labeled rooted trees ([Z6]); as well as their connections and applications to the inversion problem ([BCW],[E4]) and specializations of NCSFs ([Z5],[Z7]). In this paper, inspired by the seminal work [GKLLRT] on NCSFs (noncommutative symmetric functions), we first formulate the notion {\it ${\mathcal N}$CS systems} over associative $\mathbb Q$-algebras. We then prove some results for ${\mathcal N}$CS systems in general; the ${\mathcal N}$CS systems over bialgebras or Hopf algebras; and the universal ${\mathcal N}$CS system formed by the generating functions of certain NCSFs in [GKLLRT]. Finally, we review some of the main results that will be proved in the followed papers [Z4], [Z6] and [Z7] as some supporting examples for the general discussions given in this paper.
Zhao Wenhua
No associations
LandOfFree
Noncommutative Symmetric Systems over Associative Algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Noncommutative Symmetric Systems over Associative Algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Noncommutative Symmetric Systems over Associative Algebras will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-215882