Symmetric functions, noncommutative symmetric functions, and quasisymmetric functions II
Quantum Algebra
2007-05-23 v1 Algebraic Geometry
Abstract
Like its precursor this paper is concerned with the Hopf algebra of noncommutative symmetric functions and its graded dual, the Hopf algebra of quasisymmetric functions. It complements and extends the previous paper but is also selfcontained. Here we concentrate on explicit descriptions (constructions) of a basis of the Lie algebra of primitives of NSymm and an explicit free polynomial basis of QSymm. As before everything is done over the integers. As applications the matter of the existence of suitable analogues of Frobenius and Verschiebung morphisms is discussed.
Keywords
Cite
@article{arxiv.math/0410470,
title = {Symmetric functions, noncommutative symmetric functions, and quasisymmetric functions II},
author = {Michiel Hazewinkel},
journal= {arXiv preprint arXiv:math/0410470},
year = {2007}
}
Comments
This is part two of this survey; to appear in Acta. Appl. Math. The first part appeared in Acta Appl. Math 75 (2003), 55-93 and is also 'arXived'. 21 pages