Symmetric functions, noncommutative symmetric functions, and quasisymmetric functions II

Details Symmetric functions, noncommutative symmetric functions, and quasisymmetric functions II Symmetric functions, noncommutative symmetric functions, and quasisymmetric functions II

2004-10-21

arxiv.org/abs/math/0410470v1

Mathematics

Quantum Algebra

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 an

Scientific paper

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.

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