Noncommutative Symmetric Systems over Associative Algebras
| dc.creator | Zhao, Wenhua | |
| dc.date | 2005-09-07 | |
| dc.date | 2007-07-31 | |
| dc.date.accessioned | 2026-07-07T12:36:38Z | |
| dc.date.available | 2026-07-07T12:36:38Z | |
| dc.description | 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. | |
| dc.description | A connection of NCS systems with combinatorial Hopf algebras of M. Aguiar, N. Bergeron and F. Sottile has been added in Remark 2.17. Latex, 32 pages | |
| dc.identifier | https://arxiv.org/abs/math/0509133 | |
| dc.identifier | http://arxiv.org/abs/math/0509133 | |
| dc.identifier | J. Pure Appl. Algebra, 210 (2007), no. 2, 363--382 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/218157 | |
| dc.subject | Combinatorics | |
| dc.subject | Quantum Algebra | |
| dc.subject | 05E05, 14R10, 16W30 (Primary) 16W20, 06A11 (Secondary) | |
| dc.title | Noncommutative Symmetric Systems over Associative Algebras | |
| dc.type | text |