2004/10/21 by Michiel Hazewinkel, Hazewinkel, Michiel
Mathematics · #05E05 #05E10 #14L05 #16W30 #20C30 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.AG #math.QA #msc:05E05 #msc:05E10 #msc:14L05 #msc:16W30 #msc:20C30
paper · pdf · doi:10.48550/arxiv.math/0410470
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
arxiv created 2004/10/21 · openalex publication_date 2004/10/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.