Symmetric functions, noncommutative symmetric functions and quasisymmetric functions II

被引：10

作者：

Hazewinkel, M ^{[1
]}

机构：

[1] CWI, NL-1090 GB Amsterdam, Netherlands

来源：

ACTA APPLICANDAE MATHEMATICAE | 2005年 / 85卷 / 1-3期

关键词：

symmetric function; quasisymmetric function; noncommutative symmetric function; Hopf algebra; divided power sequence; endomorphism of Hopf algebras; automorphism of Hopf algebras; Frobenius operation; Verschiebung operation; Adams operator; power sum; Newton primitive; Solomon descent algebra; cofree coalgebra; free algebra; dual Hopf algebra; lambda-ring; Leibniz Hopf algebra; Lie Hopf algebra; Lie polynomial; formal group; primitive of a Hopf algebra; shuffle algebra; overlapping shuffle algebra;

D O I：

10.1007/s10440-004-5635-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：319 / 340

页数：22

共 48 条

[1]

[Anonymous], 1992, FUNKC ANAL PRILOZH

[2] HOMOMORPHISMS BETWEEN SOLOMON DESCENT ALGEBRAS [J].