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The primitives of the Hopf algebra of noncommutative symmetric functions

Michiel Hazewinkel
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Abstract

Let NSymm be the Hopf algebra of noncommutative symmetric functions over the integers. In this paper a description is given of its Lie algebra of primitives over the integers, Prim(NSymm), in terms of recursion formulas. For each of the primitives of a basis of Prim(NSymm), indexed by Lyndon words, there is a recursively given divided power series over it. This gives another proof of the theorem that the algebra of quasi-symmetric functions is free over the integers.

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Michiel Hazewinkel. 2004-10-16. The primitives of the Hopf algebra of noncommutative symmetric functions. https://arxiv.org/abs/math/0410365

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